Answer to Question #137870 in Classical Mechanics for Ashley

Question

A certain color emerges at 15° in the first-order spectrum. At what angle would this same color
emerge in the second order if the same source and grating are used?

Answer 1

Solution

Using following equation

$n\lambda=a sin\theta$ ................. eq. 1

For first case using

n=1, $\theta=15^°$

$\frac{\lambda}{a}=sin 15^°=0.2588$

Now for second all things are same $\lambda$ and a, n=2 and $\theta$ is finding through equation 1

$2\lambda=asin\theta$

$\sin\theta=\frac{2\lambda}{a}=2\times0.2588$

$\theta=$ $\arcsin(0.518) =31.17^°$

Therefore angle is $31.17^°$