Question

A parallel beam of monochromatic light of wavelength 5000 Å is incident normally on a single narrow slit of width 0.001 mm. The light is focussed by a convex lens on a screen placed on the focal plane. The first minimum will be formed for the angle of diffraction equal to
1. 0°
2. 15°
3. 30°
4. 50°

Answer 1

Correct Answer - Option 3 : 30°

CONCEPT:

Diffraction of Light: 

• The phenomenon of bending of waves around the corners of an obstacle/aperture of the size of the wavelength of a wave is called diffraction.
• ​Diffraction is the characteristic of all types of waves.
• The greater the wavelength of the wave higher will be its degree of diffraction.
• The condition of diffraction is that the width of the obstacle must be less than or comparable with the wavelength of the wave.

Types of diffraction:

1. Fresnel diffraction
2. Fraunhofer diffraction

Fraunhofer diffraction:

• In this type of diffraction, both source and screen are effectively at an infinite distance from the diffracting surface.
• In Fraunhofer diffraction, the plane wavefront is incident on the slit.
• In Fraunhofer diffraction, the diffraction pattern consists of a central bright fringe surrounded by dark and bright lines.
• The angle of diffraction for the n^th minima is given as,

\(⇒ sin\theta=\frac{nλ}{b}\)

Where λ = wavelength and b = width of the slit

EXPLANATION:

Given n = 1, λ = 5000 Å =5000×10^-10 m and b = 0.001 mm = 0.0010×10-3 m

• We know that the angle of diffraction for the nth minima is given as,

\(⇒ sin\theta=\frac{nλ}{b}\)

\(⇒ sin \theta =\frac{1\times5000× 10^{-10}}{.001× 10^{-3}}\)

\(⇒ sin \theta =\frac{1}{2}\)

⇒ θ = 30º

• Hence, option 3 is correct.