Question

13 A narrow beam of monochromatic light is incident normally on a diffraction grating.
Third-order diffracted beams are formed at angles of 45° to the original direction.
What is the highest order of diffracted beam produced by this grating?
A) 3rd
C) 5th
B) 4th
D) 6th
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Answer 1

Explanation:

For diffraction grating: d sinθ = nλ

When n = 3 (third order), θ = 45°

d sin45° = 3λ

d / λ = 3 / sin45°

For the highest order of diffracted beam, the angle θ should be less (or equal to) 90°. So, consider the angle θ = 90°.

d sin90° = nλ

n = (d / λ) sin90° = [3sin90°] / sin45° = 4.24.

The order n should be an integer which is less than this.

So, highest order n = 4th

Answer 2

Explanation:

SOLUTION: The diffracted light has maxima at angles dsin   m  given by Here d is grating period, m is order of diffraction and So, the highest order of diffraction: m  max dsin  max  As diffracted beam is formed at an angle of 45: dsin45 3 d   332      sin 452 3 2 4.24 So, the highest order of diffraction is m  max dsin  max  4.24 sin    max  m 4(because sin 1) ANSWER: 4