MUMBAI / AKOLA / DELHI / KOLKATA / GHAZIABAD / NASHIK / GOA / BOKARO / PUNE
IIT – JEE: 2021
TIME: 1 Hr.
Assignment (Physics)
TOPIC: Ray Wave Optics
DATE: / /21
MARKS:
MULTIPLE CORRECT ANSWER(S) TYPE
This section contains 15 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D) for its answer, out which ONE OR MORE is/are correct.
(+4, –2)
Partial Marks: +1 For darkening a bubble corresponding to each correct option. Provided NO
incorrect option is darkened. In all other cases, minus (–2) mark will be awarded in these parts.
For Example: If (A), (C)and (D)are all the correct options for a question, darkening all these
three will result in +4 marks; darkening only (A)and (D)will result in +2marks; and
darkening (A)and (B)will result in –2 marks, as a wrong option is also darkened.
1.
A student performed the experiment to measure the focal length of convex (converging) lens by lens
displacement method.(First an approximate estimate of the focal length was obtained by distant
object method in which a distant object was focused on the screen using the lens and the distance
between lens and screen noted as ‘f’, the focal length of the lens). The distance between the object
and screen is adjusted to be a value ‘l’. Now the lens, was moved from the object to the screen and
clear images are obtained for two positions of the lens, the first position L1, which is closer to object
and 2nd position L2 which is closer to screen. The distance between the two position
i.e L1L2 = d  say  . Let the focal length obtained be 'f0 '
(A) the values of l used are > 4f
(B) the image for position L1 of lens is diminished and that for position L2 of lens is magnified
(C) As l is increased (for more number of trials), ‘d’ also increases
(D) f 0 < f
2.
A point object 'O' is placed at focus of a diverging lens of focal length 'f'. When a
converging lens of focal length (f/2) is placed in between object and lens at distance f/2
from diverging lens then:
(A) The final image will be found at second focus of the converging lens
(B) Final image will be formal on the object itself.
(C) Final image is real.
(D) Final image is virtual
3.
Two half convex lenses of focal lengths f 1 = 16 cm and f 2 = 21 cm respectively are
placed such that their principal axes coincide. Both the lenses form image of a real
point object O on a fixed screen as shown. The distance between object and screen is
100 cm. Then pick up the correct statement(s)
f1=16cm
O
fixed screen
lens1
principal axis
lens2
f2=21cm
(A) The distance of lens1 from object O can be 20 cm
(B) The distance of lens 1 from object O can be 80 cm
(C) The distance of lens 2 from object O can be 30 cm
(D) The distance of lens 2 from object O can be 70 cm.
4.
A fish, F in the pond is at a depth of 0.8 m from water surface and is moving vertically upwards with
velocity 2ms1 . At the same instant a bird B is at a height of 6 m from water surface and is moving
downwards with velocity 3ms1 . At this instant both are on the same vertical line as shown in the
figure. Which of the following statements is/are correct?
(A) Height of B, observed by F (form itself) is equal to 5.30 m
(B) Depth of F, observed by B(from itself) is equal to 6.60 m
(C) Height of B, observed by F (From itself is equal to 8.80m
(D) None of these.
5.
The diagram below shows an object located at point P, 0.25 meter from a concave spherical mirror
with principal focus F. The focal length of the mirror is 0.10 meter
How does the image change as the object is moved from point P toward point F?
(A) Its distance from the mirror decreases
(B) The size of image decreases
(C) Its distance from the mirror increases
(D) The size of images increases
6.
In the experiment for the determination of the focal length of a concave mirror, the following reading
were noted. (u = object distance and v = image distance)
1/u
0.040
0.034
0.029
0.025
0.023
0.020
1/v
0.010
0.017
0.022
0.025
0.028
0.032
Which of the following is correct?
(A)
v
20 cm
B
450
A
20 cm
u
1/v
(B)
0.05 cm-1
0.05 cm-1
1/u
(C) the radius of curvature of the mirror is 40 cm
(D) In the option (a) if A and B were marked as 40 cm then (a) would be correct
7.
Two flat mirrors are kept an angle of  to each other. A source of light S is placed at equal distances
‘b’ from the mirrors. Find the fringe width (wave length =  ) (distance between the intersection of
mirrors and the screen = a)



 2b cos  2   a  bsec   / 2  
 

(A) 
4bsin   / 2 
(B)
  2bcos   a  bcos   / 2  
2bsin  / 2
(C)  2bcos  / 2  a  


 4bsin   / 2  
(D) (for very small  ) fringe width    a  b 
2b
8.
In Young’s double slit experiment the wave length of light was changed from
7000 A0 to 3500 A0 .While doubling the separation between the slits, which of the following is not
true for this experiment?
(A) The width of fringes changes
(B) The color of bright fringes changes
(C) The separation between successive bright fringes changes
(D) The separation between successive dark fringes remains unchanged.
9.
Y and Z are two partially reflecting thin glass sheets, a distance l a part in air. White light falls
normally on Y; the light emerging from Z is analysed by a spectrometer. A dark band is observed in
the spectrum at wavelength  . Possible values of l is / are:
(A)
(C)
n
2

n 

(B) n
1 
2  2
1
(D) n   

2
10.
In a Young’s double slit experiment, Let A and B be the two slits. Thin films of thicknesses t A and
tB having refractive indices  A and  B are placed in front of A and B respectively. If  At A   B t B ,
the central maxima will
(A) Not shift
(B) Shift towards A if tB  t A
(C) Shift towards B if tB  t A
(D) Shift towards A if t B  t A
11.
In Young’s double slit experiment when the slits are eliminated by white light.
(A) The central band will be white
(B) The interference band next to the central band will be red
(C) The interference band next to the central band will be violet
(D)A completely dark band can be seen
12.
If the first minima in a Young’s slit experiment occurs directly in front of one of the slits(distance
between slit & screen D=12 cm and distance between slits d  5 cm ) then the wavelength of the
radiation used can be:
2
4
(A) 2cm
(B) 4cm
(C) cm
(D) cm
3
3
13.
If one of the slits of a standard Young’s double slit experiment is covered by a thin parallel sided glass
slab so that it transmits only one half the light intensity of the other, then:
(A) The fringe pattern will get shifted towards the covered slit.
(B) The fringe pattern will get shifted away from the covered slit.
(C) The bright fringes will becomes less bright and the dark ones will become more bright
(D) The fringe width will remain unchanged
14.



A parallel beam of light    5000 A  is incident at an angle   30 with the normal to the slit plane


in a young’s double slit experiment. Assume that the intensity due to each slit at any point on the
screen is I0 . Point O is equidistant from S1 & S2 . The distance between slits is 1 mm
(A) the intensity at O is 4I0
(B) the intensity at O is zero
(C) the intensity at a point on the screen 4m from O is 4I0
(D) the intensity at a point on the screen 4m from O is zero
15.
A luminous point object is placed at O, whose image is formed at I as shown in figure. Line AB is the
optical axis. Which of the following statement is/are correct?
(A)If a lens is used to obtain the image, then it must be a converging lens and its optical centre will be
the intersection point of line AB and OI.
(B) If a lens is used to obtain the image, then it must be a diverging lens and its optical centre will be
the intersection point of line AB and OI
(C) If a mirror is used to obtain the image then the mirror must be concave and object and image
subtend equal angles at the pole of the mirror.
(D) I is a real image.
NUMERICAL VALUE TYPE
This section contains 10 questions. Each question is numerical value type. For each question,
enter the correct numerical value (in decimal notation, truncated/rounded-off to second
decimal place. (e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30).
Marking scheme: +4 for correct answer, 0 if not attempted and 0 in all other cases.
16.
Two point objects are placed on principal axis of a thin converging lens. One is 20 cm from the lens
and other is on the other side of lens at a distance of 40 cm from the lens. The images of both objects
coincide. The magnitude of focal length of lens is
17.
80
P
cm. Fill in the value of P.
A capillary tube is made of glass having index of refraction n =1.5 and is surrounded
by air. The outer radius of the tube is R= 6cm. The tube is filled with a liquid having
index of refraction n' =1.2 .Find the minimum internal radius r (in cm) of the tube
such that any ray that hits the outer surface of tube from air as shown should also enter
the liquid.
R
r
air
n'
n
incident
ray
18.
An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced
covering the lower half of the convex mirror. If the distance between the object and the plane mirror
is 30 cm, it is found that there is no parallax between the image formed by the two mirrors. Then the
radius of curvature of the of the convex mirror is equal to x  5 cm. Find the value of x ?
19.
A beam of diameter d is incident on a glass hemisphere as shown in figure. If the radius of curvature
of the hemisphere is very large in comparison to d, then diameter of the beam at the base of the
hemisphere will be
d/2
d
μ =1
μ=
(A)
20.
3d
4
3
2
(B) d
(C)
d
3
(D)
2d
3
An opaque sphere of radius ‘a’ is just immersed in a transparent liquid as shown in figure. A point
source is placed on the vertical diameter of the sphere at a distance a/2 from the top of the sphere.
One ray originating from the point source after refraction from the air liquid interface forms tangent
to the sphere. The angle of refraction for that particular ray is 300 . The refractive index of the liquid
is
a/2
Point source
air
a
(A)
2
3
liquid
(B)
3
5
(C)
4
5
(D)
4
7
21.
On introducing a thin sheet of mica (thickness 12 × 10–5 cm) in path of one of the interfering beams in
Young’s double slit experiment; the central fringe is shifted through a distance equal to the spacing
between successive bright fringes. Calculate the refractive index of mica  = 6 × 10–5 cm.
(A) 1.33
(B) 1.5
(C) 2.5
(D) 1.478
22.
M1 and M 2 are two plane mirror which are kept parallel to each other as shown. There is a point ‘O’
on perpendicular screen just infront of ‘S’. What should be the wavelength of light coming from
monochromatic source’S’. So that a maxima is formed at ‘O’ due to interference of reflected light
from both the mirrors. [ Consider only 1 st refelction].
(A)
23.
3d 2
D
(B)
3d 2
2D
(C)
d2
D
(D)
2d 2
D
A broad source of light 1  680 nm  illuminates normally two glass plates 120 mm long that touch at
one end and are separated by a wire 0.034 mm in diameter at the other end. The total number of bright
fringes that appear over the 120 mm distance is:
(A) 50
(B) 100
(C) 200
(D) 400
24.
In the figure an arrangement of young’s double slit experiment is shown. A parallel beam of light of
wavelength '  ' (in medium n1 ) is incident at an angle '  ' as shown. Distance S1O  S2 O . Point ‘O’ is
the origin of the coordinate system. The medium on the left and right side of the plane of slits has
refractive index n1 and n 2 respectively. Distance between the slits is d. The distance between the
screen and the plane of slits is D. Using D  1m , d  1mm,   30 ,   0.3mm, n1 
answer the following
4
10
,
, n2 
3
9
If y-coordinate of the point where the total phase difference between the interfering waves is zero, is
y   x 0 cm then x 0 is
25.
A lens of diameter 5.0 cm and focal length f  25.0 cm was cut along the diameter into two identical
halves. In the process, the layer of the lens a  1.00 mm in thickness was lost. Then the halves were put
together to form a composite lens. In it’s focal plane a narrow slit was placed, emitting monochromatic
light with wavelength   0.60 m . Behind the lens a screen was located at a distance b  50cm from
it. Find number of possible maxima.