longest wavelength

Question

Compute the longest wavelength, which can be observed in third order by a transmission diffraction grating with 6000 line/cm.

 

Answer is supposed to be 555.6 nm, please show me how to calculate.

Answer 1

Given:

1. Grating has 6000 lines/cm
2. Order (m) = 3
3. We need longest wavelength (λₘₐₓ) observable in that order.

Grating spacing d:

6000 lines/cm = 6000×10² = 6.0×10⁵ lines/m

d= 1/6.0×10⁵ = 1.667×10⁻⁶ m

Diffraction-grating equation:

mλ = dsin⁡θ

λ = dsinθ/m

For maximum wavelength, sinθ=1.

λ_max = d/m

Substitute values

λ_max = 1.667×10⁻⁶ m / 3

λ_max = 5.556 x 10^-7m or 555.6 x 10^-9m or 555.6 nm

Final Answer

λ_max = 555.6 nm