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,

$d sin\theta = N\lambda$

$\theta = sin^{-1}(\frac{N\lambda}{d})$

$\theta = sin^{-1}(\frac{2*(600*10^{-9})}{1.7*10^{-6}})$

$\theta = 44.9°$

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