Name: Brewster’s Law
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: Light is a transverse electromagnetic wave with electric field vectors vibrating in infinite directions perpendicular to the direction of propagation. Let's...

Question

Explain diffraction of light due to a single slit and illustrate formation of a pattern of fringes obtained on the screen and plot a graph showing variation of intensity with angle

θ

in single slit diffraction.

Accepted Answer

Diffraction of light at a single slit: When monochromatic light is made incident on a single slit. we get diffraction pattern on a screen placed behind the slit. The diffraction pattern contains bright and dark bands. the intensity of central band is maximum and goes on decreasing on both sides.

Explanation: Let AB be a slit of width 'a' and a parallel beam of monochromatic light is incident on it. According to Fresnel the diffraction pattern is the result of superposition of a large number of waves. starting from different points of illuminated slit.

Let $θ$ be the angle of diffraction for waves reaching at point $P$ of screen and $A N$ the perpendicular dropped from $A$ on wave diffracted from $B$ .
The path difference between rays diffracted at points $A$ and $B$ .

$∆ = B P - A P = B N$

In $∆ A N B, ∠ A N B = 90 °$

and $∠ B A N = θ$

$∴ \sin θ = \frac{B N}{A B} o r B N = A B \sin θ$

As $A B =$ Width of slit $= a$

$∴$ Path difference, $∆ = a \sin θ$ .

At the central point C of the screen, the angle $θ$ is zero. Hence the waves starting from all points of slit arrive in the same phase. This gives maximum intensity at the central point C.

The intensity of secondary maxima decreases with increase of order $n$ because with increasing $n$ ., the contribution of slit decreases.

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Explain diffraction of light due to a single slit and illustrate formation of a pattern of fringes obtained on the screen and plot a graph showing variation of intensity with angle $θ$ in single slit diffraction.

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