Question

600-nm light is incident on a diffraction grating with a ruling separation of 1.7 × 10-6 m. The second order line occurs at a diffraction angle of?

Answer 1

We will use the principle of overlap, specifically the principle of constructive interference to solve this problem. Mathematically this can be expressed as

`d sin\theta = N\lambda`

Where,

N = Number of fringes or number of repetition of the spectrum

d = Distance between slits

`\lambda =` Wavelength

`\theta =`Diffraction angle

Our values are given as

`\lambda =` 600nm

`d = 1.7*10^(-6)m`

`N = 2`

Replacing we have that the angle is,

`d sin\theta = N\lambda`

`\theta = sin^(-1)((N\lambda)/(d))`

`\theta = sin^(-1)((2*(600*10^(-9)))/(1.7*10^(-6)))`

`\theta = 44.9°`

Therefore the second order line occurs at a diffraction angle of 44.9°