DIFFRACTION OF LIGHT

DEFINATION
To all outward appearance, light seems to travel in straight line. A very careful observation,
however, reveals that light does suffer some deviation from its straight path when it passes close
to the edges of opaque obstacles or narrow slits. It is found that some light bends into the region
of geometrical shadow.

The bending of light around corners and spreading of light waves into the geometrical shadow
of an object is called diffraction.

The deviation of light is very small when the dimensions of the obstacle or aperture are large, as
compared to the wavelength of light and becomes much pronounced when the dimensions of the
obstacle or the aperture are comparable with the wavelength of light.

Diffraction phenomenon can conveniently be divided into two groups

(i) Fresnel diffraction phenomena and

(ii) Fraunhofer diffraction phenomena.

(i) Fresnel diffraction: In the Fresnel class of diffraction, the source of light, or the screen or
both are at finite distances from the diffracting aperture. No lenses are employed here for
rendering the light beam parallel or convergent. It turns out that it is much easier to calculate the
intensity distribution of a Fraunhofer diffraction pattern.

(ii) Fraunhofer diffraction: In the Fraunhofer class of diffraction, the source of light and the
screen are at infinite distances from the diffracting aperture. This is very conveniently achieved by
placing the source on the focal plane of a convex lens and placing the screen on the focal plane of
another convex lens. The first beam makes the light beam parallel and the second lens makes the

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 screen receive a parallel beam of light, thus effectively moving both the source and the screen to
infinity.

Difference between Fresnel and Fraunhofer diffraction phenomena:

Fresnel diffraction phenomena Fraunhofer diffraction phenomena

1. The source or the screen or both are at finite 1. The source and the screen on which the
distances from the aperture or obstacle causing pattern is observed are at infinite distances
diffraction. from aperture or the obstacle causing
diffraction.

2. In this case, the effect at a specific point on the 2. Fraunhofer diffraction pattern can be easily
screen due to the exposed incident wavefront is observed in practice.
considered. 3. The incoming light is rendered parallel with
3. No modification is made by lenses and mirrors. a lens and the diffracted beam is focused on
Observation of Fresnel diffraction phenomena the screen with another lens.
do not require any lens.

2
FRAUNHOFER DIFFRACTION AT A SINGLE SLIT

L1 L2 M
X A C
L θ Q
R
S θ P
a O x
θ
V P’
Y B
T

Fig: 1

S is a narrow slit perpendicular to the plane of the paper and illuminated by monochromatic light.
L1 is the collimating lens and AB is a slit of width a. XY is the incident spherical waterfront. The
light passing through the slit AB is incident on the lens L2 and finally refracted beam is observed
on the screen MN. The screen is perpendicular to the plane of the paper. The line SP is
perpendicular to the screen. L1 and L2 are achromatic lenses.

A plane wave front is incident on the slit AB and each point on this wave front is a source of
secondary disturbance. The secondary waves travelling in the direction parallel to OP. AQ and BV
come to focus at P and a bright central image is observed. Now, consider the secondary waves
travelling in the direction AR, inclined at an angle θ to the direction OP. All the secondary wave
travelling in this direction reach the point P’ on the screen.

The point P’ will be of maximum or minimum intensity depending on the path difference between
the secondary waves originating from the corresponding points of the wavefront.

Draw OC and BL perpendicular to AR.

Then, in the ∆ ABL

sin θ = AL/ AB = AL/ a

or AL = a sin θ

AL is the path difference between the secondary waves originating from A and B.

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If this path difference is equal to λ the wavelength of light used, then P’ will be a point of minimum
intensity.

The whole wavefront can be considered to be of two halves OA and OB and if the path difference
between the secondary waves from A and B is λ , then the path difference between the secondary
waves from A and O will be λ/2.

Similarly for every point in the upper half OA, there is a corresponding point in the lower half OB
and the path difference between the secondary waves from these points is λ/2.

Thus, the destructive interference takes place and the point P’ will be of minimum intensity.

In general, 𝑎 sin 𝜃𝑛 = 𝑛𝜆
𝑛𝜆
or, sin 𝜃𝑛 = ; whereθ gives the direction of the nth minimum and n is an integer.
𝑎

𝜆
If, the path difference is odd multiples of , the directions of the secondary maxima can be
2
𝜆
obtained. In this case, a sin 𝜃𝑛 = (2𝑛 + 1) 2

(2𝑛+1)𝜆
sin 𝜃𝑛 = ; where n =1,2,3,……
2𝑎

Thus, the diffraction pattern due to a single slit consists of a central bright maximum at P followed
by secondary maximum and minimum on both the sides.

The intensity distribution on the screen is given in fig-2. P corresponds to the position of the central
bright maximum and the points on the screen for which the path difference between the points A
and B is λ, 2λ etc., correspond to the positions of secondary minima. The secondary maxima are
of much less intensity. The intensity falls off rapidly from the point P outwards.

Fig: 2

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If the lens L2 is very near the slit or the screen is far away from the lens L2, then
𝑥
sin θ = 𝑓 ………………………………(i)

Where, f is the focal length of the lens L2

𝜆
But, sin θ = 𝑎 ……………………………………(ii)

𝑥 𝜆
so , =𝑎
𝑓

𝑓𝜆
𝑥= ;
𝑎

x is the distance of the secondary minimum from the point.

Thus the width of the central maximum = 2x.

2𝑓𝜆
2𝑥 = ………………………………(iii)
𝑎

The width of the central maximum is proportional to λ, the wavelength of light.

Ex: 1 Find the half angular width of the central bright maximum in the Fraunhofer diffraction
pattern of a slit of width 12x 10-5 cm when the slit is illuminated by monochromatic light of
wavelength 6000 A0.

Ex: 2 Fraunhofer diffraction due to a narrow slit a screen is placed 2m away from the lens to
obtain the pattern. If the slit width is 0.2 mm and the first minima lie 5 mm on either side of the
central maximum, find the wave length of light.