Question

A diffraction grating produces a first-order maximum at an angle of $20.0°$. What is the angle of the second-order maximum?

Short answer

Angle of the second order maximum is$43.2°$.

Step-by-step solution

Formula for diffraction angle

The diffraction grating's $\mathrm{m}$-th order diffraction angle is given by

${\mathrm{sin\theta }}_{\mathrm{m}}=\frac{\mathrm{m\lambda }}{\mathrm{d}}$

Where,

${\mathrm{\theta }}_{\mathrm{m}}$is angle of diffraction.

$\mathrm{d}$is grating spacing

$\mathrm{\lambda }$is wavelength

Calculation of angle of the second order

When we know that ${\mathrm{\theta }}_1=20°$

${\mathrm{\theta }}_1$is first order maximum.

The angle of second order maximum is,

${\mathrm{\theta }}_2={\sin }^{-1}\left(2\sin \left(20°\right)\right)$

$={\sin }^{-1}(0.684)$

$=43.2°$