Question

Can someone please tell me how to solve the question below. Thank you!! If 550-nm light is incident normally on a diffraction grating and exactly 6 lines are produced, the ruling separation must be:

Answer 1

The ruling separation must be between 2.2 × 10⁻⁶ m and 3.3 × 10⁻⁶ m

Step-by-step explanation:

Fringe spacing w = λ·D/s

Diffraction grating, d·sin(θ) = n·λ

n = Number of lines

When θ = 90°, we have, sin(θ) = sin(90°) = 1

Therefore;

d·sin(θ) = d × 1 = d = n·λ

When n = 6 lines and d = 550-nm, we have;

d = 6 × 550-nm = 3,300 nm = 3.3 microns = 3.3 × 10⁻⁶ m

Therefore, the ruling separation must be between 2.2 × 10⁻⁶ m and 3.3 × 10⁻⁶ m.