Answer to Question #285648 in Optics for NICKO

Question

If a diffraction grating produces a third-order bright spot for red light (of wavelength 700 nm) at 65.0° from the central maximum, at what angle will the second-order bright spot be for violet light (of wavelength 400 nm)?

Answer 1

$\theta _3=65.0°$

$\lambda_1 =700nm =700×10^{-9}m$

$\lambda _2=400nm=400×10^{-9}m$

We know that angular position of a bright band is given by

$Sin\theta_m=\frac{m\lambda}{d}$

For the third-order bright band,in the first wavelength $\lambda _1$ whereas $m$ $=+-3$

$Sin\theta _3=\frac{3\lambda_1}{d}$

$d=\frac{3\lambda_1}{Sin\theta_3}$

$d=\frac{3×700×10^{-9}}{Sin65.0°}$

$d=2.32×10^{-6}m$

$Sin\theta_2=\frac{2\lambda_2}{d}$

Hence

$\theta_2=Sin^{-1}[\frac{2\lambda2}{d}]$

$\theta_2=Sin^{-1}[\frac{2×400×10^{-9}}{2.32×10^{-6}}]$

$\theta_2=20.2°$