Chapter 36: Diffraction
Questions and Example Problems
sin   1.22
a sin   md  (md  1, 2,3,...)

d
2
a
 sin  
Isin gle slit ()  Im 
sin 
 , 

  
2
d
 sin  
I double slit ( )  Im  cos   
sin 
 , 

  
2
d sin   mc 
 mc
d
1
a
 mc ,
d
 0,1,2,... 
N
Example 36.1
A single-slit diffraction experiment is set up with light of wavelength 420 nm, incident
perpendicularly on a slit of width 5.10 μm. The viewing screen is 3.20 m distant. (a)
Draw a picture of the situation that shows, angles θm, md and ∆r/. On the screen, (b) what is
the distance between the first and second diffraction minimas from center of the diffraction
pattern? (b) What are the widths of the central diffraction maxima and the first secondary
diffraction maxima?
Example 36.2
A slit 0.240 mm side is illuminate by 540 nm light. The diffraction pattern is observed on a
screen that is 3.00 m from the slit. The intensity at the center of the central maximum is
6.00×10-6 W/m2.
a. What is the distance on the screen from the center of the central maximum to the first
diffraction minima?
b. What is the intensity at a point on the screen midway between the center of the central
maximum and the first minimum?
Example 36.3
A beam of light of a single wavelength is incident perpendicularly on a double-slit arrangement.
The slit widths are each 46 m and the slit separation is 0.30 mm. How many complete bright
fringes appear between the two first-order minima of the diffraction pattern?
33-1
Example 36.4
In the two-slit interference experiment the slit widths are each 12.0 m, their separation is 24.0
m, the wavelength is 600 nm, and the viewing screen is at a distance of 4.00 m. Let Ip
represent the intensity at point P on the screen, at height y = 70.0 cm.
a. What is the ratio of Ip/Im at the center of the pattern?
b. Determine where P is in the two-slit interference pattern by giving the maximum or minimum
on which it lies or the maximum and minimum between which it lies.
c. Next, for the diffraction that occurs, determine where point P is in the diffraction pattern by
giving the minimum on which it lies or the two minima between which it lies.
Problem 36.5
In a two-slit interference pattern, what is the ratio of slit separation to slit width if there are 17
bright fringes within the central diffraction envelope and the diffraction minima coincide with
two-slit interference maxima?
Problem 36.6
A diffraction grating 20.0 mm wide has 6000 rulings. Light of wavelength 589 nm is incident
perpendicularly on the grating. What are the (a) largest, (b) second largest, and (c) third
largest values of θ at which maxima appear on a distant viewing screen?
33-2