Diffraction Problems-2014 [Year]

1. A slit of width a is illuminated by white light. For what value of a does the first minimum for
red light ( = 650nm) fall at u = 15
o
?
2. In the previous problem, what is the wavelength of the light whose first diffraction maximum
(not counting the central maximum) falls at 15
o
, thus coinciding with the first minimum of red
light?
3. When monochromatic light is incident on a slit 0.022 mm wide, the first diffraction
minimum is observed at an angle of 1.8
0
from the direction of the incident beam. Find
the wavelength of the incident light.
4. Determine the maximum slit width that could be used if a central maximum angular
width of 0.12 mrad can just be detected and you guess the wavelength of the x-rays to
be 0.10 nm.
5. Monochromatic light of wavelength 441 nm falls on a narrow slit. On a screen 2.16 m
away, the distance between the second minimum and the central maximum is 1.62 cm.
(a) Calculate the angle of diffraction of the second minimum, (b) Find width of the slit.
6. Light of wavelength 633 nm is incident on a narrow slit. The angle between the first
minimum on one side of the central maximum and the first minimum on the other side
is 1.97
0
. Find the width of the slit.
7. A single slit is illuminated by light whose wavelengths are a and
b
, so chosen that the
first diffraction minimum of the a component coincides with the second minimum of
the
b
component. (a)What relationship exists between the two wavelengths? (b) Do
any other minima in the a patterns coincide?
8. A plane wave, with wavelength of 593 nm, falls on a slit of width 420 m. A thin
converging lens having a focal length of 71.4 cm, is placed behind the slit and focuses
the light on a screen. Find the distance on the screen from the slits from the center of
the pattern to the second minimum.
9. In a single slit diffraction pattern, the distance between the first minimum on the right
and the first minimum on the left is 5.20mm. The screen on which pattern is displayed is
82.3cm from the slit and the wavelength is 546nm. Calculate the slit width.
10. The distance between the first and the fifth minima of a single slit pattern is 0.350mm
with the screen 41.3 cm away from the slit, using light having a wavelength of 546 nm.
(a) Calculate the diffraction angle of the first minimum. (b) Find the width of the slit.
11. A slit 1.16mm wide is illuminated by light of wavelength 589 nm. The diffraction pattern
is seen on screen 2.94m away. Find the distance between the first two diffraction
minima on the same side of the central maximum.
12. Calculate, approximately, the relative intensities of the maxima in the single slit Fraunhofer
diffraction pattern.
13. Monochromatic light with wavelength 538 nm falls on a slit with width 25.2m. The
distance from the slit to a screen is 3.48m. Consider a point on the screen 1.13cm from
Diffraction Problems-2014 [Year]

the central maximum. Calculate (a) u (b) o (c) ratio of the intensity at this point to the
intensity at the central maximum.
14. An astronaut in a satellite claims to be able to just barely resolve two point sources on
Earth, 163 km below. Calculate the (a) angular (b) linear separation of the two point
sources, assuming ideal conditions. Take =540 nm and the pupil diameter of the
astronauts eye to be 4.90 mm.





15. The two headlights of an approaching automobile are 1.4 m apart. Assume the pupil
diameter is 5.0 mm and the wavelength of light is 550 nm. (a) At what angular
separation and (b)minimum distance will the eye resolve them?
16. The wall of a large room is covered with acoustic tile in which small holes are drilled
5.20 mm from the center. How far can a person be from such a tile and still distinguish
the individual holes, assuming ideal conditions? Assume the diameter of the pupil of the
observers eye to be 4.60 mm and the wavelength to be 542 nm .
17. Find the separation of two points on the Moons surface that can just be resolved by
200-in ( 5.08 m) telescope at Mount Palomar, assuming that this distance is determined
by diffraction effects. Assume a wavelength of 565 nm. Given D= 3.84 x 10
8
m
18. If superman really had x-ray vision at 0.12 nm wavelength and a 4.3 mm pupil diameter,
at what maximum altitude could he distinguish villains from heroes assuming the
minimum detail required was 4.8 cm?
19. The painting contains small dots (~2 mm in diameter) of pure pigment, as indicated in
figure. The illusion of color mixing occurs because the pupils of the observers eyes
diffract light entering them. Calculate the minimum distance an observer must stand
from painting to achieve the desired blending of color. (wavelength = 475nm, diameter
of pupil = 4.4mm)



Diffraction Problems-2014 [Year]

20. Two slits of width a and separation d are illuminated by a coherent beam of light of
wavelength . What is the linear separation of the interference fringes observed on a
screen that is distance D away?
21. For d =2a in the following figure, how many interference
fringes lie in the central diffraction envelope?
(b) If we put d=a, the two slits coalesce into a slit of
width 2a. Show that equation
reduces to diffraction pattern for a single slit.
22. (a) Design a double slit system in which the fourth fringe, not counting the central
maximum, is missing. (b) What order fringes, if any are also missing?
23. How many complete fringes appear between the first minima of the fringe envelope on
either side of the central maximum for a double-slit pattern if = 557 nm, d = 0.150
mm, and a = 0.030 mm? (b) What is the ratio of the intensity of the third fringe to the side of
the center to that of the central fringe?
24. What requirements must be met for the central maximum of the envelope of the
double-slit interference pattern to contain exactly 11 fringes?
25. Suppose that, as In Problem 24, the envelope of central peak contains 11 fringes. How
many fringes lie between the first and second minima of the envelope.
26. Light of wavelength 440nm passes through a double slit,
wielding the diffraction pattern of intensity I versus
deflection angle shown in Figure. Calculate (a) the slit width
and (b) the slit separation. (c) Verify the displayed intensities
of m=1 and m=2 interference fringes.
27. . A certain grating has 10
4
slits with a spacing of d = 2100 nm.
It is illuminated with yellow sodium light ( = 589 nm).
Find (a) the angular position of all principal maxima
observed and (b) the angular width of the largest order
maximum.
28. Light of wavelength 600 nm is incident normally on
a diffraction grating. Two adjacent principal maxima occur
at sin u = 0.20 and sin u = 0.30. The fourth order is missing.
(a) what is the separation between adjacent slits?
(b) what is the smallest possible individual slit width?
(c) Name all orders actually appearing on the screen with the values derived in (a) & (b).
29. A grating has 315 rulings / mm. For what wavelengths in the visible spectrum can fifth-
order diffraction be observed?
( )
2
2
(

| I =
u

si n
cos
m
I
Diffraction Problems-2014 [Year]

30. Given a grating with 400 rulings/mm, how many orders of the entire visible spectrum
(400-700nm) can be produced?
31. White light (400 nm < < 700 nm) is incident on a grating . Show that, no matter what
the value of the grating spacing d, the second- and third-order spectra overlap.
32. A diffraction grating has 1.20 X 10
4
rulings uniformly spaced over a width W = 2.50cm. It
is illuminated at normal incidence by yellow light from a sodium vapor lamp. This light
contains two closely spaced lines of wavelengths 589.0 nm and 589.59 nm. (a) At what
angle does the first maximum occur for the first of these wavelengths? (b) What is the
angular separation between these two lines (1
st
order)? (c) How close in wavelength can
two lines be (in first order) and still be resolved by this grating? (d) How many rulings
can a grating have and just resolve the sodium doublet line?
33. A grating has 9600 lines uniformly spaced over a width 3cm and is illuminated by
mercury light.
(a)What is the expected dispersion in the third order, in the vicinity of intense green line
( = 546nm)? (b)What is the resolving power of this grating in the fifth order? (c) What
is the wavelength difference that can be resolved in the 5
th
order.
34. The sodium doublet in the spectrum of sodium is a pair of lines with wavelengths 589.0
and 589.6 nm. Calculate the minimum number of rulings in a grating needed to resolve
this doublet in the second-order spectrum.
35. In a particular grating, the sodium doublet is viewed in third order at 10.2 to the
normal and is barely resolved. Find (a) the ruling spacing and (b) the total width of
grating.