Diffraction of light
9.1. Introduction
The Dutch scientist Christian Huygens proposed a wave theory of light that
provides a useful technique he developed for predicting the future position of a wave
front when an earlier position is known. This is known as Huygens’ principle and can
be stated as follows: Every point on a wave front can be considered as a source of tiny
wavelets that spread out in the forward direction at the speed of the wave itself. The
new wave front is the envelope of all the wavelets – that is, the tangent to all of them.
A large number of equally spaced parallel slits is called a diffraction grating,
although the term ”interference grating” might be as well appropriate. Gratings can be
made by precision machining of a very fine parallel lines on a glass plate. The
untouched spaces between the lines serve as the slits. Photographic transparencies of
an original grating serve as inexpensive gratings. Gratings containing 10 000 lines per
centimetre are common today, and are very useful for precise measurements of
wavelengths. A diffraction grating containing slits is called a transmission grating.
Reflection gratings are also used, which are made by ruling fine lines on a metallic or
glass surface from which light is reflected and analyzed. The analysis is basically the
same as for a transmission grating, which we now discuss.
The analysis of a diffraction grating is much like that of Young’s double-slit
experiment. We assume parallel rays of light are incident on the grating as shown in
Fig. 9.1. We also assume that the slits are narrow enough so that diffraction by each of
them spreads light over a very wide angle on a distant screen behind the grating, and
interference can occur with light from all the other slits. Light rays that pass through
each slit without deviation (θ=0) interfere constructively to produce a bright line at the
centre of the screen. Constructive interference also occurs at an angle  such that the
rays from adjacent slits travel an extra distance of ∆l=mλ, where m is an integer. Thus,
if d is the distance between slits, then we see from Fig. 9.1 that ∆l=dsinθ, and
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DIFFRACTION OF LIGHT
sin  
m
, m  0,1,2,
d
principal
maxima

(9.1)
is the criterion to have a brightness maximum. This is the same equation as for the
double-slit situation, and again m is called the order of the pattern.
l =d sin 
d
l

Fig. 9.1 Diffraction grating.
9.2. Measurements
9.2.1. Calculation of wavelength
Switch on the laser and set the diffraction grating ( d = 10 μm) perpendicularly to the
direction of the ray of laser light. The effect of interference of rays bent on the
diffraction grating can be seen as a pattern of light dots on the screen. The pattern is
symmetrical with respect to the zero-order dot.
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DIFFRACTION OF LIGHT
Screen
Laser
Diffraction grating
Fig. 9.2 Experimental setup.
Measure the distance of the diffraction grating from the screen and the distances of the
series of interferential maxima from the zero-order dot (“zeroth maximum” on the
figure). That allows to measure angles of diffraction for these maxima (on both sides
of the incident beam). If the angles differ by less than 5 degrees, then the position of
the diffraction grating should be appropriately corrected. Compose your setup and
repeat the measurements 6 times.
The diffraction grating has a known constant, hence wavelength λ of a light source can
be easily determined, from the equation (9.1). The data should be collected in the Table
9.1.
1st
maximum
1st
minimum

1st
maximum
P’
x
A
Zeroth
maximum
1st
minimum
Zeroth
maximum
C


B
P
Diffraction
scale
1st
minimum
L
Diffraction grating
Retina of
your eye
1st
maximum
Fig. 9.3. Diffraction of a light.
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DIFFRACTION OF LIGHT
9.2.2. Diffraction grating constant
Switch on the laser and set next diffraction grating perpendicularly to the direction of
the ray of laser light. Measure the distance L of the diffraction grating from the screen
and the distances of the series of interferential maxima from the zero-order dot
(“zeroth maximum” on the figure) l1, l2, l3, l4, and so on. That allows to measure angles
of diffraction for these maxima (on both sides of the incident beam). Measurements
should be repeated 6 times.The light source has a known wavelength λ from the first
part, hence diffraction grating constant d can be easily determined, from the equation
(9.1). The data should be collected in the Table 9.1.
9.2.3. Hair width
This experiment is similar to the previous one, because the diffraction can be observed
on any thin obstacle like human hair. The result is also obtained in the similar
procedure by measuring the angles of diffraction for several orders of the pattern. The
data should be collected in the Table 9.1.
Table 9.1.
Order of pattern
L
l
 [nm]
d [m]
a[m]
m
1
2
3
4
9.3. Results, calculation and uncertainty
From the data collected in the table calculate the average values of the wavelength λ of
a light source, diffraction grating constant d and hair width a. Estimate the uncertainty
of the measured values using method of standard deviation.
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DIFFRACTION OF LIGHT
The final results reads:
    S
(9.2)
d  d  Sd
(9.3)
a  a  Sa
(9.4)
9.4. Questions
1. Formulate the Huygens’ principle. What can you predict using this principle?
2. Discuss Young’s double – slit experiment.
3. What kind of physical phenomena can you observe on diffraction grating?
4. What are the conditions for diffraction and interference?
5. Discuss Bragg’s equation.
6. What is geometric optics? What is physical optics?
7. Explain rainbow phenomenon.
8. Can you give examples of diffraction gratings implementation ?
9. What is a laser? How is laser light different from ordinary light? What are lasers used
for?
10. What are electromagnetic waves? Discuss polarization phenomena .
9.5. References
1. Dryński T., Ćwiczenia laboratoryjne z fizyki, PWN, Warszawa, 1959
2. Resnick R., Halliday D., Fizyka, Tom 2, PWN, Warszawa, 1989.
3. Szydłowski H., Pracownia fizyczna, PWN, Warszawa, 1994.
4. Young H.D., Freedman R.A., University Physics with Modern Physics,
Addison-Wesley Publishing Company, 2000
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