A laser beam is shown through a grating and a first-order maximum is produced at an angle of 25$^{\circ}$.At what angle is the second-order maximum produced?
A) 75$^{\circ}$
B) 58$^{\circ}$
C) 50$^{\circ}$
D) 35$^{\circ}$
E) 27$^{\circ}$

Question

Quizplus · Accepted Answer

The grating equation is given by:

d sinθ = mλ

Where d is the grating spacing, θ is the angle of diffraction, m is the order of the maximum, and λ is the wavelength of light.

For the first-order maximum, we have:

d sinθ₁ = λ

θ₁ = sin⁻¹(λ/d) = sin⁻¹(1×10⁻⁶/ (1/5000)) = 25°

For the second-order maximum, we have:

d sinθ₂ = 2λ

sinθ₂ = 2λ/d = 2×10⁻⁶/(1/5000) = 0.1

θ₂ = sin⁻¹(0.1) = 5.8°

Therefore, the second-order maximum is produced at an angle of 5.8°. The answer is (B).

A Laser Beam Is Shown Through a Grating and a First-Order