Optics
Unit VI: Optics
Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and
its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lens-maker’s
formula. Magnification, power of a lens, combination of thin lenses in contact. Refraction and dispersion of
light through a prism.
Scattering of light - blue colour of the sky and reddish appearance of the sun at sunrise and sunset.
Optical instruments: Human eye, image formation and accommodation, correction of eye defects (myopia,
hypermetropia, presbyopia and astigmatism) using lenses. Microscopes and astronomical telescopes
(reflecting and refracting) and their magnifying powers.
Wave optics: wave front and Huygens’ principle, reflection and refraction of plane wave at a plane surface
using wave fronts. Proof of laws of reflection and refraction using Huygens’ principle. Interference, Young’s
double slit experiment and expression for fringe width, coherent sources and sustained interference of light.
Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical
telescopes. Polarisation, plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids.
[1993]
Q.1
Q.2
The two slits in Young’s double slit experiment are separated by a distance of 0.2 mm, an interference
pattern is produced on a screen 1.5 m away. The 4th dark fringe is a distance of 1.8 cm from the
central maximum. Calculate the wavelength of light used.
Determine the angular separation between central maximum and first order maximum of the
diffraction pattern due to a single slit of width 0.25 mm when light of wavelength 5890 Å is incident
on it normally.
[1995]
Q.1
Explain why white light dispersed when passing through a prism.
[1996]
Q.1
Q.2
Q.3
A ray of light when moves from denser to rarer medium undergoes total internal reflection. Derive the
expression for critical angle in terms of speed of light in the respective media.
How can you distinguish between an unpolarised light and a linearly polarized light beam using a
polarised.
Light of wavelength 600 nm is incident on an aperture of size. Calculate the distance upto which the
ray of light can travel such that its spread is less than the size of the aperture.
[1997]
Q.1
Q.2
Refractive index of glass for light of yellow, green and red colours are ny , ng and nr respectively.
Rerrange these symbols in an increasing order of values.
An astronomical telescope of magnifying power 10 consists of two thin lenses 55 cm apart. Calculate
the focal lengths of the lenses.
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Q.3
A glass prism of refracting angle 60 and refractive index 1.5 is immersed in water of refractive index
1.33. Calculate the angle of minimum deviation of the prism in this situation. [(sin-1 (0.56) = 34.3]
[1998]
Q.1
Q.2
Q.3
Q.4
Q.5
Why is the interference pattern not detected, when two coherent sources are far apart?
Why no interference pattern is observed when two coherent sources are (i) infinitely close (ii) Far
apart from each other.
Two coherent sources whose intensity ratio is 81: 1 produce interference fringes. Calculate the ratio of
intensity of maxima and minima in fringe system.
A slit of width d is illuminated by light of wavelength, 5500 Å. What will be the value of slit width ‘a’
when
(a)
first minimum falls at an angle of diffraction 30?
(b)
First maximum falls at an angle of diffraction 30?
No interference pattern is detected when two coherent sources are infinitely close to each other. Why?
[1999]
Q.1
Q.2
Q.3
In which direction relative to normal does array of light bend when it enters obliquely in a medium in
which its speed is reduced.
For the same angle of incidence the angels of refraction in three different media A, B and C are 15,
25 and 35 respectively. In which medium the velocity of light is minimum?
A converging lens has a focal length of 20 cm in air. It is made of a material of refractive index 1.6. If
it is immersed in a liquid of refractive index 1.3, what will be the new focal length?
[2000]
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
When light undergoes refraction, what happens to its frequency?
How does the frequency of a beam of ultraviolet light change when it goes from air to glass?
What is the ratio of velocities of light of wavelength 4000 Å and 8000 Å in vacuum?
A convex lens made of a material of refractive index n1 is kept in a medium of refractive index n2.
parallel rays of light are incident on the lens
(i) n1 > n2
(ii) n1 = n2 (iii) n1 < n2
A convex mirror and a convex lens are held in water. What changes, if any, do you expect in their
respective focal lengths as compared to their values in air.
Describe a compound microscope and find an expression for its magnifying power.
Laser light of wavelength 630 nm inciden is immersed in water of refractive index 1.33. Calculate the
angle of minimum t on a pair of slits produces an interference pattern in which bright fringes are
separated by 8.1 mm. A second light produces an interference pattern in which the fringes are
separated by 7.2 mm. Calculate the wavelength of the second light.
A double concave lens of glass of refractive index 1.6 has radii of curvature 40 cm and 60 cm.
Calculate its focal length.
[2001]
Q.1
Q.2
Sketch the variation of intensity of the intererenfce pattern in Young’s double slit experiment.
Draw a graph showing the variation of intensity of polarised light transmitted by an analysis.
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[2002]
Q.1
The refractive index of a material of convex lens is n1. It immersed in a medium of refractive index n2.
A parallel beam of light is incident on the lens. Trace the path of the emergent rays when n2 > n1.
n2
Q.2
n2
In the figure given below the path of a parallel beam of light passing through a convex lens of
refractive index ng kept in a medium of refractive index nm is shown. Is (i) ng = nm (ii) ng > nm (iii) ng
< nm?
nm
Q.3
n1
ng
nm
In the fig. given below the path of a parallel beam of light passing through a convex lens of refractive
index ng kept in medium of refractive index nm is shown. Is
nm
(i) ng = nm
(ii) ng > nm (iii) ng < nm
nm
ng
Q.4
Q.5
Q.6
Q.7
The polarizing angle of a medium is 60. What is the refractive index of the medium?
The refractive index of a material is 3. What is the angle of refraction if the unpolarised light is
incident on it at the polarizing angle of the medium?
State the condition for total internal reflection. Calculate the speed of light in medium whose critical
angle is 45?
Give reasons for following observations made from earth
(i)
Sum is visible before the actual sun rise.
(ii)
Sun looks reddish at sum set.
[2003]
Q.1
Q.2
Q.3
Q.4
Two slits in Young’s double slit experiment are illuminated by two different lamps emitting light
same wavelength. Will you observe the interference pattern? Justify your answer.
An object is placed at the focus of a concave lens. Where will its image be formed?
Give two differences between interference and diffraction of light.
Draw a graph to show the angle of deviation  with the variation of angle of incidence i for a
monochromatic ray of light passing through a prism of refracting angle a. Deduce the relation
relation n = sin A + m/2  sin A/2
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Q.5
A converging lens of focal length 6.25 cm is used as a magnifying glass. If the near the point of the
observer is 25 cm from the eye and lens is held close to eye, calculate (i) the distance of the object
from the les (ii) angular magnification when final image is formed at infinity.
Q.1
Violet light is incident on a thin convex lens. If this light is replaced by red light, explain with reason,
how the power of the lens would change?
Draw a ray diagram of an astronomical telescope in the near point adjustment. Write down the
expression for its magnifying power.
State two conditions for sustained interference of light.
Write the sign conventions used. What happens to the focal length of convex lens when it is immersed
in water?
Briefly explain, how the focal length of a convex lens changes, with increases in wave length of
incident light.
A compound microscope with an objective of 1.0 cm focal length and an eye piece of 2.0 cm focal
length has a tube length of 20 cm. Calculate the magnifying power of the microscope, if the final
image is formed at the near point of the eye.
In Young’s double slit experiment, using light of wavelength, 400 nm, interference fringes of width
‘X’ are obtained. The wavelength of light is increased to 600 nm and the separation between the slits
is halved. If one wants the observed fringe width on the screen to be same in the two cases, find the
ratio of the distance between the screen and the plane of interfering source with two arrangements.
Find the ratio of intensities at two points on a screen in Young’s double slit experiment when waves
from the two slits have a path difference of (i) 0 and (ii) /4.
Light of wavelength 500 nm falls, from a distant source, on a slit 0.50 mm wide. Find the distance
between the tow dark bands, on either side of the central bright band, of the diffraction pattern
observed, on a screen placed 2m from the slits.
[2004]
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
Q.8
Q.9
[2005]
Q.1
Q.2
Q.3
Sate Huygen’s Principle. With the help of suitable diagram. Prove Snell’s law of refraction using
Huygen’s wave theory
The image of a candle is formed by a convex lens on a screen. The lower half of the lens is painted
black to make it completely opaque. Draw the ray diagram to show the image formation. How will
this image be different from the one obtained when the lens is not painted black?
How is a wavefront different from a ray? Draw the geometrical shape of the wavefronts when (i) light
diverges from a point source, and (ii) light emerges out of a convex lens when a point source is placed
at its focus.
[2006]
Q.1
Q.2
Q.3
Draw a labeled diagram of reflecting type telescope. Write its any one advantage over refracting type
telescope.
What is interference of light? Write two essential conditions for sustained interference pattern to be
produced on the screen.
Draw a graph showing the variation of intensity versus the position on the screen Young’s experiment
when (a) both the slits are opened and (b) one of the slits is closed.
What is the effect on the interference pattern in Young’s double slit experiment when:
(i)
screen is moved closer to the plane of slits? (ii) Separation between two slits is increased.
Explain your answer in each case.
What are coherent sources of light? State two conditions for two light sources to be coherent.
Derive a mathematical expression for the width of interference fringes obtained in Young’s double slit
experiment with the help of a suitable diagram.
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Q.4
A beam of light converges to a point P.A lens is placed in the path of the convergent beam 12 cm
from P. At what point does the beam converge if the lens is (a) a convex of focal length 20 cm, (b) a
concave lens of focal length 16 cm.
[2007]
Q.1
Q.2
Q.3
Q.4
Q.5
Define resolving power of a compound microscope. How does the resolving power of a compound
microscope change when?
(i)
refractive index of the medium between the object and objective lens increases?
(ii)
Wavelength of the radiation used is increased?
A double convex lens of glass of refractive index 1.6 has its both surfaces of equal radii of curvature
of 30 cm each. An object of height 5 cm is placed at a distance of 12.5 cm from the lens. Calculate the
size of the image formed.
State the essential condition for diffraction of light to take place.
Use Huygens’principle to explain diffraction of light due to a narrow single slit and the formation of a
pattern of fringes obtained on the screen. Sketch the pattern of fringes formed due to diffraction at a
single slit showing variation of intensity with angel .
OR
What are coherent sources of light? Why are coherent sources required to obtain sustained
interference pattern?
State three characteristic feature which distinguish the interference pattern due to two coherently
illuminated sources as compared to that observed in a diffraction pattern due to a single slit.
A converging lens has a focal length of 20 cm in air. It is made of a material of refractive index 1.5. If
it is immersed in water of refractive index 4/3, what will be the new focal length?
State the condition under which the phenomenon of diffraction of light takes place. Derive an
expression for the width of the central maximum due to diffraction of light at a single slit.
[2008]
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
How does the angle of minimum deviation of a glass prism vary, if the incident violet light is replaced
with red light?
Why does the bluish colour predominate in a clear sky?
Draw a labeled ray diagram of an astronomical telescope in the near point position. Write the
expression for its magnifying power.
Sate one feature by which the phenomenon of interference can be distinguished from that of
diffraction.
A parallel beam of light of wavelength 600 mm is incident normally on a slit of width ‘a’. If the
distance between the slits and the screen is 0.8 m and the distance of 2nd order maximum from the
center of the screen is 15 mm, calculate the width of the slit.
Distinguish between unpolariesed and plane polarized light. An unpolarised light is incident on the
boundary between two transparent media. Sate the condition when the reflected wave is totally plane
polarized. Find out the expression for the angle of incidence in this case.
Derive the fens formula,
1 1 1
  for a concave lens, using the necessary ray diagram.
f v u
Two lenses of powers 10D and –5D are placed in contact.
(i)
Calculate the power of the new lens.
(ii)
Where should an object be held from the lens, so as to obtain a virtual image of magnification 2?
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What are coherent sources of light? Two slits in Young’s double slit experiment are
illuminated by two different sodium lamps emitting light of the same wavelength. Why is
no interference pattern observed?
(b)
Obtain the condition for getting dark and bright fringes in Young’s experiment. Hence
write the expression for the fringe width.
(c)
If a is the size of the source and d its distance from the plane of the two slit. What should
be the criterion for the interference fringes to be seen?
Why must both the objective and eyepiece of a compound microscope have short focal lengths?
When viewing through a compound microscope, our eyes should be positioned not on the eye-piece
but a short distance away from it for best viewing, why? How much should be that short distance
between the eye and eye-piece?
An object is placed at the principal focus of a concave lens of focal length . Where will its image be
formed?
How does the power of a convex lens vary, if the incident red light is replace by violet light?
A glass lens of refractive index 1.5 is placed in a trough of liquid. What must be the refractive index
of the liquid in order to make the lens disappear?
A converging lens of refractive index 1.5 is kept in a liquid medium having same refractive index.
What is the focal length of the lens in this medium?
A diverging lens of focal length ‘F’ is cut into two identical parts, each forming a plano concave lens.
What is the focal length of each part?
What is the geometrical shape of the wavefront when a plane wave passes through a convex lens?
(a)
Q.7
Q.8
Q.9
Q.10
Q.11
Q.12
Q.13
Q.14
F
Q.15 How does the angular separation of interference fringes change in Young’s experiment, if the distance
between the slits is increased?
Q.16 How does the fringe width of interference fringes change, when the whole apparatus of young’s
experiment is kept in a liquid of refractive index 1.3?
Q.17 Draw a ray diagram showing how the final image of a distant object using an astronomical telescope
in the normal adjustment position. Write mathematical expression for its magnifying power. How
does the magnifying power get affected on increasing the aperture of the objective lens and why?
Q.18 Show a labeled ray diagram showing the formation image in a compound microscope. Write the
expression for its magnifying power.
Q.19 State two conditions for sustained interference of light.
Q.20 How will the angular separation and visibility of fringes in Young’s double slit experiment change
when (i) screen is moved away from the plane of the slits. (ii) Width of source slit is increased.
Q.21 In a single slit experiment, the width of the slit is made double the original width. How does this affect
the size and intensity of the central diffraction band? Draw a plot of the intensity distribution.
Q.22 If a light beam shows no intensity variation when transmitted through a polaorid which is rotated;
does it mean that the light is unploarised? Explain briefly.
Q.23 Explain with the help of a diagram, how the above principle is used for transmission of video signals
using optical fibers.
Q.24 Describe a compound microscope and find an expression for its magnifying power.
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Q.25 Draw a graph to show the angle of deviation  with the variation of angle of incidence i for a
monochromatic ray of light passing through a prism of refracting angle A. Deduce the relation
n = sin A + m/2 ∕ sin A/2
Q.26 How is a wavefront defined? Using Huygens’s construction draw figure showing the propagation of a
plane wave reflecting at the interface of the two media. Show that the angle of incidence is equal to
angle of reflection.
Q.27 A compound microscope consists of an objective lens of focal length 2.0 cm and an eyepiece of focal
length 6.25 cm separated by a distance of 15 cm. How far from the objective should an object be
placed in order to obtain the final image at (i) the least distance of distinct vision (D = 25 cm) and (ii)
infinity.
What is the magnifying power of the microscope in each case?
Q.28 (a)
A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an
eye-piece of focal length 15m. If an eye-piece of focal length 1.0 cm is used, what is the
angular magnification of the telescope?
(b)
If this telescope is used to view the moon, what is the diameter of the image of the moon
formed by the objective lens? The diameter of the moon is 3.48 × 106 m and radius of lunar
orbit is 3.8 × 106 m.
Moon
Objective Lens
D

Image of moon

r
d
f0
Q.29 Calculate the distance of an object of height ‘h’ from a concave mirror or focal length 10 cm, so as to
obtain a real image of magnification 2.
Q.30 A converging lens of refractive index 1.5 and of focal length 15 cm in air, has the same radii of
curvature for both sides. If it is immersed in a liquid of refractive index 1.7, find the focal length of
the lens in the liquid.
Q.31 A ray of light passing through an equilateral triangular prism from air undergoes minimum deviation
when angle of incidence is ¾ th of the angle of prism. Calculate the speed of light in the prism.
Q.32 A diverging lens of refractive index 1.5 and of focal length 20 cm in air has the same radii of
curvature for both sides. If it is immersed in a liquid of refractive index 1.7, calculate the focal length
of lens in the liquid.
[2009]
Q.1
Q.2
Q.3
Q.4
Two thin lenses of power +5 D and -2 ·5 D are in contact. What is the focal length of the
combination?
[1]
How would the angular separation of interference fringes in Young's double slit experiment change
when the distance between the slits and screen is halved?
[1]
(i)
What is the relation between critical angle and refractive index of a material?
(ii)
Does critical angle depend on the colour of light? Explain.
[2]
Define the term 'linearly polarised light'.
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Q.5
Q.6
When does the intensity of transmitted light become maximum, when a polaroid sheet is rotated
between two crossed polaroids?
[2]
In Young’s’ double slit experiment, monochromatic light of wavelength 600 nm illuminates the pair
of slits and produces an interference pattern in which two consecutive bright fringes are separated by
10 mm. Another source of monochromatic light produces the interference pattern in which the two
consecutive bright fringes are separated by 8 mm. Find the wavelength of light from the second
source.
What is the effect on the interference fringes if the monochromatic source is replaced by a source of
white light?
[3]
(a)
(i)
Draw a labeled diagram to show the formation of image in an astronomical
telescope for a distant object.
(ii)
Write three distinct advantages of a reflecting type telescope over a refracting type
telescope.
(b)
A convex lens of focal length 10 cm is placed coaxially 5 cm away from a concave lens of
focal length 10 cm. If an object is placed 30 cm in front of the convex lens, find the position of
the final image formed by the combined system.
[5]
Or
(a)
With the help of a suitable ray diagram, derive the mirror formula for a concave mirror.
(b)
The near point of a hypermetropic person is 50 cm from the eye. What is the power of the lens
require to enable the person to read clearly a book held at 25 cm from the eye?
[5]
[2010]
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
A converging lens is kept coaxially in contact with a diverging lens both the lenses being of equal
focal lengths. What is the focal length of the combination?
[1]
When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed
Imply a decrease in the energy carried by the light wave? Justify your answer.
[1]
(i)
Draw a net labeled ray diagram of an astronomical telescope in normal
adjustment. Explain
briefly its working.
(ii)
An astronomical telescope uses two lenses of powers 10 D and 1 D. What is its magnifying
power in normal adjustment?
[3]
Or
(i)
Draw a neat labeled ray diagram of a compound microscope. Explain briefly its working.
(ii)
Why must both the objective and the eye-piece of a compound microscope have short focal
lengths?
In Young’s double slit experiment, the two slits 0.15 mm apart are illuminated by monochromatic
light of wavelength 450 nm. The screen is 1.0 m away from the slits.
(a)
Find the distance of the second (i) bright fringe, (ii) dark fringe from the central maximum.
(b)
How will the fringe pattern change if the screen is move away from the slits?
[3]
How does an unpolarised light get polarized when passed through a Polaroid?
Two polaroids are set in crossed positions. A third Polaroid is placed between the two making an
angle  with the pass axis of the first Polaroid. Write the expression for the intensity of light
transmitted from the second Polaroid. In what orientations will the transmitted intensity be (i)
minimum and (ii) maximum?
[3]
An illuminate object and a screen are placed 90 cm apart. Determine the focal length and nature of the
lens required to produce a clear image on the screen, twice the size of the object.
[3]
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[2011]
Q.1
Q.2
Q.3
A convex lens made up of glass of refractive index 1.5 is dipped, in turn in (i) a medium of refractive
index 1.65, (ii) a medium of refractive index 1.33.
[3]
(a)
Will it behave as a converging or a diverging lens in the two cases?
(b)
How will its focal length change in the two media?
Use the mirror equation to show that
(i)
an object placed between f and 2f of a concave mirror produces a real image beyond 2f.
(ii)
an convex mirror always produces a virtual image independent of the location of the object.
(iii) an object placed between the pole and focus of a concave mirror produces a virtual and
enlarged image.
[3]
A compound microscope uses an objective lens of focal length 4 cm and eyepiece lens of focal length
10 cm. An object is placed at a 6 cm from the objective lens. Calculate the magnifying power of the
compound microscope. Also calculate the length of the microscope.
[3]
OR
A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an
eyepiece lens of focal length 1.0 cm is used, find the angular magnification of the telescope.
If this telescope is used to view the moon, what is the diameter of the image of the moon formed by
the objective lens? The diameter of the moon is 3.42 × 106 m and the radius of the lunar orbit is 3.8 ×
108 m.
Q.4
State the importance of coherent sources in the phenomenon of interference.
In Young’s double slit experiment to produce interference pattern, obtain the conditions for
constructive and destructive interference. Hence deduce the expression for the fringe width.
How does the fringe width get affected, if the entire experimental apparatus of Young is immersed in
water?
[5]
(a)
(b)
(c)
OR
State Huygens’ principle. Using this principle explain how a diffraction pattern is obtained on
a screen due to a narrow slit on which a narrow beam coming from a monochromatic source of
light is incident normally.
Show that the angular width of the first diffraction fringe is half of that of the central fringe.
If a monochromatic source of light is replaced by white light, what change would you observe
in the diffraction pattern?
[2012]
Q.1
For the same value of angle of incidence, the angles of refraction in three media A, B and C are 15 0,
250 and 350 respectively. In which medium would the velocity of light be minimum?
[1]
Q.2
In a single-slit diffraction experiment, the width of the slit is made double the original width. How
does this affect the size and intensity of the central diffraction band?
[1]
An object AB is kept in front of a concave mirror as shown in the figure.
(i)
Complete the ray diagram showing the image formation of the object.
(ii)
How will the position and intensity of the image be affected if the lower half of the mirror’s
reflecting surface is painted black?
[2]
Draw a labeled ray diagram of a reflecting telescope. Mention its two advantages over the refracting
telescope.
[2]
Q.3
Q.4
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Q.5
Q.6
You are given three lenses L1, L2 and L3 each of focal length 15 cm. An object is kept at 20 cm in
front of L1, as shown. The final real image is formed at the focus ‘I’ of L3. Find the separations
between L1, L2 and L3.
[3]
(a)
In Young’s double slit experiment, derive the condition for (i) constructive interference and
(ii) destructive interference at a point on the screen.
(b)
A beam of light consisting of two wavelength, 880 nm and 600 nm is used to obtain the
interference fringes in a Young’s double slit experiment on a screen place 1.4 m away. If the
two slits are separated by 0.28 mm, calculate the least distance from the central bright
maximum where the bright fringes of the two wavelength coincide.
OR
[5]
(a)
How does an unpolarized light incident on a Polaroid get polarized?
Describe briefly, with the help of a necessary diagram, the polarization of light by reflection
from a transparent medium.
(b)
Two polaroids ‘A’ ‘B’ are kept in crossed position. How should a third Polaroid ‘C’ be placed
between them so that the intensity of polarized light transmiteed by Polaroid B reduces to 1/8 th
of the intensity of unpolarized light incident on A?
[2013]
Q.1
A convex lens of focal length f1 is kept in contact with a concave lens of focal length f2. Find the focal
length of the combination.
Q.2
(a)
What is linearly polarized light? Describe briefly using a diagram how sunlight is polarised.
(b)
Unpolarised light is incident on a polaroid. How would the intensity of transmitted light
change when the polaroid is rotated?
Q.3
Draw a labelled ray diagram of a refracting telescope. Define its magnifying power and write the
expression for it. Write two important limitations of a refracting telescope over a reflecting type
telescope.
[2014]
Q.1
A biconvex lens made of transparent material of refractive index 1.25 is immersed in water of
refractive index 1.33. Will the lens behave as a converging or a diverging lens? Give reason.
Q.2
Two monochromatic rays of light are incident normally on the face AB of an isosceles right angled
prism ABC. The refractive indices of the glass prism for the two rays ‘1’ and ‘2’ are respectively 1.35
and 1.45. Trace the path of these rays after entering through the prism.
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Q.3
(a)
Using the phenomenon of polarization, show how transverse nature of light can
demonstrated.
be
(b)
Two polaroids P1 and P2 are placed with their pass axes perpendicular to each other.
Unpolarised light of intensity I0 is incident on P1. A third Polaroid P3 is kept in between P1 and
P2 such that its pass axis makes an angle of 30 with that of P1. Determine the intensity of light
transmitted through P1, P2 and P3.
Q.4
A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20
cm. The two are kept at 15 cm from each other. A point object lies 60 cm in front of the convex lens.
Draw a ray diagram to show the formation of the image by the combination. Determine the natural
and position of the image formed.
Q.5
An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie
wavelength associated with the electrons. Taking other factors, such as numerical aperture etc. to be
same, how does the resolving power of an electron microscope compare with that of an optical
microscope which uses yellow light?
Q.6
(a)
In Young’s double slit experiment, describe briefly how bright and dark fringes are obtained
on the screen kept in front of a double slit. Hence obtain the
expression for the fringe width.
(b)
The ratio of the intensities at minima to the maxima in the Young’s double slit
is 9 : 25. Find the ratio of the width of the two slits.
experiment
OR
(a)
Describe briefly how a diffraction pattern is obtained on a screen due to a single narrow slit
illuminated by a monochromatic source of light. Hence obtain the conditions for the angular
width of secondary maxima and secondary minima.
(b)
Two wavelengths of sodium light of 590 nm and 596 nm are used in turn to study the
diffraction taking place at a single slit of aperture 2 × 10-6 m. The distance between the slit
and the screen is 1.5 m. Calculate the separation between the positions of first maxima of the
diffraction pattern obtained in the two cases.
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SAMPLE PAPER
Q1.
Q.2
Q.3
Q.4
An incident beam of light of intensity ‘Io’ is made to fall on a Polaroid ‘A’, another Polaroid ‘B’ is so
oriented with respect to ‘A’ that there is no light emerging out of ‘B’. A third Polaroid ‘C’ is now
introduced mid-way between ‘A’ and ‘B’ and is so oriented that its axis bisects the angle between the
axes of ‘A’ and ‘B’. What is the intensity of light now between?
(i) A and C
(ii) C and B
Give reasons for your answers?
Two nearby narrow slits are illuminated by a single monochromatic source. Name the pattern obtained
on the screen?
One of the slits is now completely covered. What is the name of the pattern now obtained on
the screen?
Write two differences between the patterns obtained in the two cases?
Four double convex lenses, with the following specifications are available
Lens
Focal length
Aperture
A
100 cm.
10 cm.
B
100 cm.
5 cm.
C
10 cm.
2 cm.
D
5 cm
2 cm.
Which two of the given four lenses, should be selected as the objective and eye piece to construct an
astronomical telescope and why? What will be the magnifying power and normal length of the
telescope tube so constructed?
Write two advantages of reflecting type telescope over such a telescope?
Find the position of the image formed by the lens shown in the figure. Another lenses is placed in
contact with this lens to shift the image further away from the lens. What is the nature of the second
lens?
f =10cm
Q
O
30 cm
Q.5
Write the relation between angle of incidence (i); the angle of emergence (e), the angle of prism
(A) and the angle of deviation() for rays undergoing refraction through a prism? What is the relation
between <i and <e for rays undergoing minimum deviation? Using this relation obtain an expression
for the refractive index () of the material of the prism in terms of A and angle of minimum
deviation?
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Q6.
Following figure shows an experimental set up similar to Young’s double slit experiment to observe
interference of light.
P
S1
S
O
S2
Q.7
Q.8
Q.9
Here,
SS2- SS1= /4
Write the condition of (i) Constructive (ii) destructive Interference at any point P in terms of path
difference
 - S2P – S1P
Does the central fringe observed in the above set up lie above or below ‘O’? Given reason in support
of your answer.
Yellow light of wavelength 6000 Å produces fringes of width 0.8mm in Young’s double slit
experiment. What will be the fringe width if the light source is replaced by another monochromatic
source of wavelength 7500 Å and separation between the slits is doubled?
Define one lumen?
How dose the resolving power of a telescope change when the aperture of its objective is increased?
An equiconvex lens of focal length
15 cm is cut in to two equal halves
as shown.
What is the focal length of each half?
Q.10 Write two points of difference between interference and diffraction patterns of light?
Q.11 Calculate the refractive index of material of an equilateral prism for which the angle of minimum
deviation is 600?
Q.12 A microscope is focused on a dot at the bottom of a beaker. Some oil is poured into the beaker to a
height of ‘Y’ cm and it is found necessary to raise the microscope through a vertical distance of ‘x’
cm to bring the dot again into focus. Express refractive index of oil in terms of ‘x’ and ‘y’?
Q.13 Describe an experiment to demonstrate transverse wave nature of light?
Q.14 Define the term critical angle for a given pair of media? Establish its relationship with their relative
refractive index?
Q.15 A convex lens made up of a material of refractive index 1 is immersed in a medium of refractive
index 2. Trace the path of a parallel beam of light passing through the lens when. (i) 1 = 2
(ii) 1 < 2 . Explain your answer?
Q.16 State the Huygen’s principle? Name the type of wave front that corresponds to a beam of light.
(i)
coming from a very far-off source.
(ii)
diverging radically from a point source.
Q.17 A sunshine recorder globe of 30cm diameter is made of glass of refractive index  = 1.5. A ray enters
the globe parallel to the axis. Find the position form the centre of the sphere where the ray crosses the
axis?
Q.18 A narrow monochromatic beam of light of intensity ‘I’ is incident on a glass plate. Another identical
glass plate is kept close to fist one and parallel to it. Each plate reflects 25% if the incident light and
transmits the remaining. Calculate the ratio of minimum and maximum intensity in the interference
pattern formed by the two beams obtained after reflection form each plate?
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Q.19 How would the length of the day be affected if there were no atmosphere around the earth? Explain
your answer with the help of a diagram?
Q.20 Draw the diagram shown intensity distribution of light on the screen for diffraction of light at a single
slit. How is the width of central maxima affected on increasing the
(i)
wavelength of light used.
(ii)
width of the slit?
What happens to the width of the central maxima if the whole apparatus is immersed in water and
why?
Q.21 Which of the following waves can be polarized
(i)
x –rays
(ii)
sound waves?
Give reasons.
Two Polaroid are used to study polarization. One of them (the polariser) is kept fixed and the other
(the analyzers) is initially kept with its axis parallel to the polariser. The analyzers is then rotated
through angles of 45o, 90o and 180o in turn. How would the intensity of light coming out of analyzers
be affected for these angles of rotation, as compared to the initial intensity and why?
Q.22 A spherical surface of radius of curvature ‘R’ and of refractive index ‘2’ is placed in a medium of
refractive index ‘1’ where 1 < 2. The surface produces a real image of an object kept in front of it.
Using appropriate assumptions and sign conventions, derive a relationship between the object
distance, image distance, ‘R’, ‘1’ and ‘2’? Under what conditions this surface diverges a ray
incident on it?
Q.23 A thin prism of refracting angle l 2o deviates an incident ray through an angle of 1o. Find the value of
refractive index of the material of the prism?
Q.24 Write two differences between interference and diffraction?
Two plane monochromatic waves propagating in the same direction with amplitudes ‘A’ and ‘2A’ and
differing in phase by /3 superpose. Calculate the amplitude of the resultant wave?
Q.25 A ray of light goes from medium 1 to medium 2. Velocity of light in the two media are ‘c1’ and ‘c2’
respectively. For an angle of incidence  in medium 1, the corresponding angle of refraction in
medium 2 is /2.
(i) Which of the two media is optically denser and why?
(ii) Establish the relationship between ‘’, ‘c1’ and ‘c2’.
Q.26 Two convex lenses ‘A’ and ‘B’ of an astronomical telescope having focal lengths 5cm and 20cm
respectively, are arranged as shown in the figure.
(i)
Which one of the two lenses you will select
B
A
to use as the objective lens and why?
(ii)
What should be the change in the distance between the lenses to
have the telescope in its normal adjustment position?
15cm
(iii) Calculate the magnifying power of the telescope in the normal
adjustment position?
Q.27 The refractive index of water is 4/3. Obtain the value of the semi vertical angle of the cone within
which the entire outside view would be confined for a fish under water. Draw an appropriate ray
diagram?
Q.28 State Huygen’s principal and use it to, construct refracted wave–front for refraction of a plane wave
front at a plane-refracting surface. Hence derive Snell’s Law?
Q.29 Explain the function of the (i) collimator (ii) telescope, in a spectrometer. With the help of an
appropriate ray diagram discuss how we use a spectrometer for finding the refracting angle of a prism.
Write the formula used for determination of refractive index of the material of the prism using the
spectrometer?
Q.30 Name the wave phenomenon which is exhibited by light waves but not by the sound waves.
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Q.31 What is meant by the term ‘interference of light.’ Write any tow conditions necessary for obtaining
well-defined and sustained interference pattern of light.
Q.32 Define the term angular dispersion. Draw the path of a ray of white light passing through a prism and
mark angular dispersion on it.
Q.33 The radius of curvature of each surface of a convex lens of refractive index 1.5 is 40 cm. Calculate its
power.
Q.34 Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the
values of wavelength, frequency and speed of. (a) reflected light (b) refracted light. Refractive index
of water is 1.33.
Q.35 Using the data given below, state which two of the given lenses will you prefer to construct a best
possible (i) telescope (ii) microscope. Also indicate which of the selected lenses is to be used as an
objective and as an eyepiece in each case
Lenses
Power (P)
Aperture (A)
L1
6D
1 cm
L2
3D
8 cm
L3
10D
1 cm
Q.36 How would the angular separation of interference fringes in young’s double slit experiment change
when the distance of separation between the slits and the screen is doubled?
Q.37 How is the resolving power of a microscope affected when,
(i)
the wavelength of illuminating radiations is decreased?
(ii)
the diameter of the objective lens is decreased?
Justify your answer.
Q.38 The following data was recorded for values of object distance and the corresponding values of image
distance in the experiment on study of real image formation by a convex lens of power +5D. One of
these observations is incorrect. Indentify this observation and give reason for your choice:
S. No.
Object distance (cm)
Image distance (cm)
1
25
97
2
30
61
3
35
37
4
45
35
5
50
32
6
55
30
Q.39 A beam of light of wavelength 400 nm is incident normally on a right-angled prism as shown. It is
observed that the light just grazes along the surface AC after falling on it. Given that the refractive
index of the material of the prism varies with the wavelength  as per the relation
A=1.2+b/2
Calculate the value of b and the refractive index of the prism material for a wavelength =5000Å.
[(Given  = Sin-1 (0.625)]
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Q.40 An equiconvex lens with radii of curvature of magnitude r each is put over a liquid layer poured on
top of a plane mirror. A small needle, with its tip on the principal axis of the lens, is moved along the
axis until its inverted real image conicides with the needle itself. The distance of the needle from the
lens is measured to be ‘a’. On removing the liquid layer and repeating the experiment the distance is
found to be ‘b’.
Given that two values of distances measured represent the focal length values in the two cases, obtain
a formula for the refractive index of the liquid.
Q.41 A partially plane polarised beam of light is passed through a polaroid. Show graphically the variation
of the transmitted light intensity with angle of rotation of the polaroid.
Q.42 In a double slit interference experiment, the two coherent beams have slightly different intensities I
and I + I(I<<). Show that the resultant intensity at the maxima is nearly 4I while that at the minima
( I ) 2
is nearly
.
4I
Q.43 State the principle, which helps us to determine the shape of the wavefront at a later time from its
given shape at any time. Apply this principle to
(i)
Show that a spherical/ plane wavefront continues to propagate forward as a spherical/plane
wave front.
(ii)
Derive Snell’s law of refraction by drawing the refracted wavefront corresponding to a plane
wavefront incident on the boundary separating a rarer medium from a denser medium.
Q.44 Which two main considerations are kept in mind while designing the ‘objective’ of an astronomical
telescope?
Obtain an expression for the angular magnifying power and the length of the tube of an astronomical
telescope in its ‘normal adjustment’ position.
Q.45 (i)
Derive the mirror formula, which gives the relation between f, v and u. What is the
corresponding formula for a thin lens?
(ii)
Calculate the distance d, so that a real image of an object at O, 15cm in front of a convex lens
of focal length 10cm be formed at the same point O. The radius of curvature of the mirror is
20cm. Will the image be inverted or erect?
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Q.46 A microscope is focused on a dot at the bottom of a beaker. Some oil is poured into the beaker to a
height of ‘Y’ cm and it is found necessary to raise the microscope through a vertical distance of ‘x’
cm to bring the dot again into focus. Express refractive index of oil in terms of ‘x’ and ‘y’?
Q.47 Describe an experiment to demonstrate transverse wave nature of light?
Q.48 Define the term critical angle for a given pair of media? Establish its relationship with their relative
refractive index?
Q.49 Which two of the above four lenses should be selected as objective and eyepieces of a compound
microscope and why? How can the magnifying power of such a microscope be increased?
Draw a labelled ray diagram for the image formation in such a microscope?
Q.50 A beam of light converges at a point on the screen. A plane parallel glass plate is introduced in the
path of this converging beam. How will the point of convergence be affected? Draw the relevant ray
diagram?
Q.51 The polarization of beam of light by reflection is best achieved when the reflected and refracted rays
are right angels to each other. Show that the polarizing angle of incidence is then given by iP = tan-1

Q.52 (i)
Using the relation for refraction at a single spherical refracting surface, derive the lens maker’s
formula.
(ii)
In the accompanying diagram, the direct image formed by the lens (f = 10cm) of an object
placed of O and that formed after reflection from the spherical mirror are formed at the same
point. What is the radius of curvature of the mirror?
Q.53 A concave mirror, of aperture 4cm, has a point object placed on its principal axis at a distance of
10 cm from the mirror. The image, formed by the mirror, is not likely to be a sharp image. State the
likely reason for the same.
[1]
Q.54 The following table gives data about the single slit diffraction experiment:
Wave length of Light
Half Angular width of the principal maxima


p
q
Find the ratio of the widths of the slits used in the two cases. Would the ratio of the half angular
widths of the first secondary maxima, in the two cases, be also equal to q?
[2]
Q.55 A monochromatic source, emitting light of wave length, 600 nm, has a power output of 66W.
Calculate the number of photons emitted by this source in 2 minutes.
[2]
Q.56 Three identical polaroid sheets P1, P2, and P3 are oriented so that the (pass) axis of P2 and P3 are
inclined at angles of 600 and 900, respectively, with respect to the (pass) axis of P1. A monochromatic
source, S, of intensity I0, is kept in front of the polaroid sheet P1. Find the intensity of this light, as
observed by observers O1, O2, and O3, positioned as shown below.
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Q.57 Draw an appropriate ray diagram to show the passage of a ‘white ray’, incident on one of the two
refracting faces of a prism. State the relation for the angle of deviation, for a prism of small refracting
angle.
It is known that the refractive index, , of the material of a prism, depends on the wavelength, , of
the incident radiation as per the relation
m= A +
B
l2
where A and B are constants. Plot a graph showing the dependence of  on  and identify the pair of
variables, that can be used here, to get a straight line graph.
[3]
Q.58 (a)
Write the formula for the velocity of light in a material medium of relative permittivity r and
relative magnetic permeability r.
[1]
(b)
The following table gives the wavelength range of some constituents of the electromagnetic
spectrum.
S.No.
Wavelength Range
1mm to 700nm
0.1m to 1mm
400 nm to 1nm
< 10-3 nm
Select the wavelength range, and name the (associated) electromagnetic waves, that are used in
(i)
(ii)
Radar systems for Aircraft navigation
Earth satellites to observe growth of crops.
[2]
Q.59 (i)
A thin lens, having two surfaces of radii of curvature r1 and r2, made from a material of
refractive index  2, is kept in a medium of refractive index 1 . Derive the Lens Maker’s
formula for this ‘set-up’
(ii)
A convex lens is placed over a plane mirror. A pin is now positioned so that there is no
parallax between the pin and its image formed by this lens-mirror combination. How can this
observation be used to find the focal length of the convex lens? Give appropriate reasons in
support of your answer.
OR
The figure, drawn here, shows a modified Young’s double slit experimental set up. If SS2 - SS1,= /4,
(i)
state the condition for constructive and destructive interference
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(ii)
(iii)
obtain an expression for the fringe width.
locate the position of the central fringe.
[5]
Q.60 A magician during a show makes a concave glass lens with refractive index 1.47 changes into convex
lens while dipping it in another medium.
What will be the ratio of refractive index of glass with that of the medium?
[1]
Q.61 A beam of light coming out of a convex lens when a point source is placed at its focus is incident on
an equilateral prism. Draw the shape of wave fronts coming out of the convex lens and the prism. [2]
Q.62 State the condition for diffraction of light to occur.
The following table gives data about the single slit diffraction experiment:
Wave length of Light
Half Angular width of
the principal maxima
Λ
Θ
Pλ
Qθ
Find the ratio of the width of the slits used in the two cases. Would the ratio of the half angular width
of the first secondary maxima, in the two cases, be also equal to Q?
[3]
Q.63 Two slits in Young’s experiment are illuminated by a monochromatic lamp. With a neat sketch, get an
expression for fringe width of the interference pattern so obtained.
[3]
How will the fringe width change when the region between coherent sources and the screen is filled
with another medium of refractive index ’μ’.
[3]
Q.64 Trace the path of three rays from a distant object through an astronomical telescope in normal
adjustment.
(a)
The far point of a myopic person is 80 cm in front of the eye. What is the power of the lens
required to enable him to see very distant objects clearly?
(b)
In what way does the corrective lens help the above person?
(c)
The above person prefers to remove his spectacles while reading a book. Why?
OR
(a)
A ray of light is normally incident on one face of an equilateral prism. Trace the course of the
ray through the prism and emerging from it.
(b)
The critical angle for glass-air interface is ‘ic’. Will the critical angle for glass-water interface
be greater than or less than ‘ic ’? Why?
(c)
How does the angle of minimum deviation of a glass prism change if the incident violet light is
replaced by red light?
[5]
Q.65 What should be the nature of the lens and the position of the object if we want its image to be upright,
virtual and magnified by a factor 0 < m < 1?
Q.66 Consider interference between two sources of intensities I and 4I. What will be the intensity at points
where phase differences is (1)  (2) 
Q.67 Derive Snell’s law on the basis of Huygen’s wave theory.
Q.68 Explain with reason, how the resolving power of a compound microscope will change when
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(i)
frequency of the incident light on the objective lens is increased.
(ii)
focal length of the objective lens is increased.
(iii)
aperture of objective lens is increased.
Q.69 Draw a graph to show the angle of deviation with the angle of incidence i for a monochromatic ray of
light passing through a prism of refracting angle A.
Deduce the relation
OR
Define diffraction. Deduce an expression for fringe width of the central maxima of the diffraction
pattern, produced by single slit illuminated with monochromatic light source.
(
)
Q.70 A ray of light, incident on an equilateral glass prism mglass = 3 moves parallel to the base of the
prism, inside it.
Q.71 The intensity, at the central maxima (O) in a Young’s double slit set up is I0. If the distance OP equals
one third of the fringe width of the pattern, show that the intensity, at point P, would equal I0/4.
Q.72 An object is placed at a distance of 15 cm from a convex lens of focal length 10 cm. On the other side
of the lens, a convex mirror is placed such that its distance, form the lens, equals the focal length of
the lens. The image formed by this combination is observed to coincide with the object itself. Find the
focal length of the convex mirror.
Q.73 Two convex lenses, of equal length, but of aperture A1 and A2 (A2 < A1), are used as the objective
lenses in two astronomical telescopes having identical eyepieces.
Compare the ratio of their (i) resolving power (ii) (normal) magnifying power and (iii) intensity of
images formed by them. Which one of the two telescopes should be preferred? Why?
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Q.74 (a)
A plane wave front approaches a plane surface separating two media. If medium on is
(optically) denser and medium two is (optically) rarer, construct the refracted wave front using
Huygens’ principle.
(b)
Draw the shape of the refracted wave front when a plane wave front incident on (i) prism and
(ii) convex mirror. Give a brief explanation for the construction.
OR
(a)
(b)
State the essential condition for the diffraction of light to take place.
A parallel beam of monochromatic light falls normally on a narrow slit and light coming out of the slit
is obtained on the screen. Derive an expression for the angular width of the centre bright maxima
obtained on the screen.
‘Diffraction defines the limit of the ray optics.’ Give a brief explanation of this statement.
Q.75 How will the intensity of maxima and minima, in the Young’s double slit experiment change, if one of
the two slits is covered by a transparent paper which transmits only half of the light intensity?
Q.76 A light beam is incident on the boundary between two transparent media. At a particular angle of
incidence the reflected ray is perpendicular to the refracted ray. Obtain an expression for this angle of
incidence. Does this angle depend on the wavelength of light used?
Q.77 In the double slit experiment, the patterns on the screen is actually a superposition of single slit
diffraction from each slit and the double slit interference pattern. In what way is the diffraction from
each slit related to the interference pattern in a double slit experiment?
Explain.
Hence draw the intensity distribution curve, obtained on the screen, in the double slit experiment
(i)
(ii)
When the width of each slit is comparable to wavelength of monochromatic light used
When the width of each slit is relatively large compared to wave length of monochromatic light.
Q.78 A 5 cm long needle is placed 10 cm from a convex mirror of focal length 40 cm. Find the position,
nature and size of the image of the needle.
What happens to the size of image when the needle is moved farther away from the mirror?
Q.79 Draw a ray diagram for a compound microscope. Derive an expression for the magnifying power
when the final image is formed at the least distance of distinct vision. State the expression for the
magnifying power when the image is formed at infinity. Why is the focal length of the objective lens
of a compound microscope kept quite small?
OR
Derive the lens formula giving the relation between u, v, and f for a thin convex lens. Define the term
‘linear magnification’ and draw a graph showing the variation of linear magnification with image
distance for a thin con vex lens. How can this graph be used for finding the focal length of the lens?
Q.80 A plane wave front, of width X, is incident on an air-water interface and the corresponding refracted
wavefront has a width Z as shown. Express the refractive index of air with respect to water in terms of
the dimension shown.
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Q.81 A device X can convert one form of energy into another. Another device Y can be regarded as a
combination of a transmitter and a receiver. Name the devices X and Y.
Q.82 A luminescent object is placed at a depth ‘d’ in a (optically) denser medium of refractive index ‘’.
Prove that radius r, of the base of the cone or light, from the object, that can emerge out from the
surface, is
r=
d
m2 -1
Q.83 A slit of width ‘d’ is illuminated by white light. For what value of ‘d’ is the first minimum, for red
light of = 650 nm, located at point P? For what value of the wave length of light will the first
diffraction maxima also fall at P?
Q.84 Give reason for each of the following observations :
(i)
The resultant intensity at any point on the screen varies between zero and four times the
intensity, due to one slit, in Young’s double slit experiment.
(ii)
A few coloured fringes, around a central white region, are observed on the screen, when the
source of monochromatic light is replaced by white light in Young’s double slit experiment.
(iii)
The intensity of light transmitted by a Polaroid is half the intensity of the light incident on it.
Q.85 A plot between the angle of deviation () and angle of incidence (i), for a triangular prism is shown
below.
Explain why any given value of ‘’ corresponds to two values of angle of incidence? State the
significance of point ‘P’ on the graph. Use this information to derive an expression for refractive
index of the material of the prism.
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OR
A thin lens, made of material of refractive index , has a focal length ‘f’. If the lens is placed in a
transparent medium of refractive index ‘n’ (n < ), obtain an expression for the change in the focal
length of the lens. Use the result to show that the focal length of a lens of the glass ( = g) becomes
mw ( mg -1)
times its focal length in air, when it is place in water ( = W).
( mg - mw )
What happens when n > . Explain using appropriate ray diagram.
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