“If you lead me astray, then my wanderIngs wIll brIng me to my destInatIon.”
1. A single slit of width 0.5 mm is illuminated with monochromatic light (λ=680
nm). A screen is placed 1.8 m from the slit to observe the fringe pattern.
 What is the angle between the second dark fringe (m=2) and the
central maximum?
 What is the lateral displacement of this dark fringe?
2. Light of wavelength 750 nm passes through a slit 1.0 x 10–3 mm wide. How
wide is the central maximum?
 in degrees, and
 in centimeters, on a screen 20 cm away?
3. Determine the angular positions of the first- and second-order lines (maxima)
for light of wavelength 400 nm and 700 nm incident on a grating containing
10,000 slits per centimeter.
4. White light containing wavelengths from 400 nm to 750 nm strikes a grating
containing 4000 slits/cm. Show that the blue at l = 450 nm of the third-order
spectrum overlaps the red at 700 nm of the second order.
5. Light emitted by hot hydrogen gas is observed with a spectroscope using a
diffraction grating having The spectral lines nearest to the center (0°) are a
violet line at 24.2°, a blue line at 25.7°, a blue-green line at 29.1°, and a red line
at 41.0° from the center. What are the wavelengths of these spectral lines of
hydrogen?
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6. A parallel beam of light of wavelength 500 nm falls on a narrow slit and the
resulting diffraction pattern is observed on a screen 1 m away. It is observed
the first minimum is at a distance of 2.5 mm from the centre of the screen.
Find the width of the slit.
7. In a single slit diffraction pattern, the distance between the first minimum on
the right and the first minimum on the left is 5.2mm. The screen on which the
pattern is displayed is 80cm from the slit and the wavelength used is
546nmcalculate the slit width.
8. A slit 1.0mm wide is illuminated by light of wavelength 589nm. We see a
diffraction pattern on a screen 3.0m away. What is the distance between
the first two diffraction minima on either side of the central diffraction
maximum?
9. Plane waves of wavelength 600nm fall normally on a slit of width 0.2mm.
Calculate the linear and angular width of the central maximum on a
screen 2 m away from the slit.
10. Figure below is a graph of the intensity of light of wavelength as a function
of the distance y along a screen for a single-slit diffraction pattern with slit
width a. Copy this graph in your answer sheet and sketch on it a graph of
intensity as a function of the distance along the screen for (a) light of
wavelength  / 2 and slit width a (Label it a) and (b) light of wavelength  and
slit width a/2 (Label it b).
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11. Derive the half-width of the central maximum in a single-slit Fraunhofer
diffraction. The half-width is the angle between the two points in the
pattern where the intensity is one-half that at the centre of the pattern. If
the width of the slit is 5 times the wavelength what is the half-width?
12. A screen is placed 50cm from a single slit, which is illuminated with 690nm
light. If the distance between the first and third minima in the diffraction
pattern is 3.0mm, what is the width of the slit?
13. A diffraction pattern is formed on a screen 120cm away from a 0.40mm-wide
slit. Monochromatic 546.1-nm light is used. Calculate the fractional intensity
at a point on the screen 4.1mm from the center of the principal maximum.
14. A single slit of width 3.0 μm is illuminated by a sodium yellow light of
wavelength 589 nm. Find the intensity at a 15° angle to the axis in terms of the
intensity of the central maximum.
15. A single slit of width 0.1 mm is illuminated by a mercury light of wavelength
576 nm. Find the intensity at a 10° angle to the axis in terms of the intensity of
the central maximum.
16. At what angle is the first minimum for 550-nm light falling on a single slit of
width 1.00 μm? (b) Will there be a second minimum?
17. The width of the central peak in a single-slit diffraction pattern is 5.0 mm. The
wavelength of the light is 600 nm, and the screen is 2.0 m from the slit. (a) What
is the width of the slit? (b) Determine the ratio of the intensity at 4.5 mm from
the center of the pattern to the intensity at the center.
18. An aircraft maintenance technician walks past a tall hangar door that acts like
a single slit for sound entering the hangar. Outside the door, on a line
perpendicular to the opening in the door, a jet engine makes a 600-Hz sound.
At what angle with the door will the technician observe the first minimum in
sound intensity if the vertical opening is 0.800 m wide and the speed of sound
is 340 m/s?
19. What is the minimum width of a single slit (in multiples of λ) that will produce
a first minimum for a wavelength λ? What is its minimum width if it produces
50 minima? 1000 minima?
20. Consider the single-slit diffraction pattern for λ = 600 nm, D = 0.025 mm, and x
= 2.0 m. Find the intensity in terms of I0 at θ = 0.5°, 1.0°, 1.5°, 3.0°, and 10.0°.
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21. A double slit produces a diffraction pattern that is a combination of single- and
double-slit interference. Find the ratio of the width of the slits to the separation
between them, if the first minimum of the single-slit pattern falls on the fifth
maximum of the double-slit pattern. (This will greatly reduce the intensity of
the fifth maximum.)
22. Sodium emits visible light with a wavelength of 589 nm. This light is passed
through a diffraction grating of 300 lines per mm. Calculate the angular
separation between the first line to the left of the central image and the first
line to the right of the central image.
23. Coherent laser light of wavelength 633 nm is incident on a single slit of width
0.25 mm. The observation screen is 2.0 m from the slit.
 What is the width of the central bright fringe?
 What is the width of the bright fringe between the 5th and 6th
minima?
24. A woman is walking along a straight path, which is at right angles to a
telephone line, as shown in the diagram below. Two birds are perched on the
line, 0.40 m apart.
The diameter of the pupil of the woman’s eye is 2.5 mm and the average
wavelength of visible light is 550 nm. Use the Rayleigh criterion to
estimate the distance D at which the woman will just be able to see two
separate birds.
25. If the pupil of your eye can open as much as 5 mm, in diameter, what is the
smallest distance you can resolve on a piece of paper 30 cm away, using light
with l = 600 nm?
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26.
A monochromatic wave of wavelength k illuminates a two-slit system as
shown above in the figure. The diffraction pattern is recorded on a screen a
distance L from the two slits plane. You may assume k<< d, D << L. In
terms of the given variables;
 What is the distance A between adjacent interference fringes observed
on the screen?
 What is the width DX of the central lobe of the diffraction pattern on the
screen?
27. The diffraction pattern shown below is produced by passing He-Ne laser light
(λ= 632.8 nm) through a single slit and viewing the pattern on a screen 1.00 m
behind the slit. What is the width of the slit?
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