Question

White light is incident onto a $30°$prism at the $40°angle$shown in Figure $p35.41$. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is $20\%$larger than the index of refraction of red light. At what $angle\varphi$does red light emerges from the rear face?

Short answer

$\delta =1.02°$

Step-by-step solution

Given information

Given:

$Red=\delta ={\delta }_R-{\delta }_v=30.72-30.04$

$\delta =0.68°$

Simplification

$n_1\sin \delta =n_2\sin {\delta }_2$

${\delta }_2={\sin }^{-1}\left(\frac{n_1\sin \delta }{n_2}\right)$

$n_1=1.00n_2=1.53\leftarrow violet1.50x1.02$

${\delta }_1=50{\delta }_2=30.04°$

${\delta }_2={\sin }^{-1}\left(\frac{n_1\sin {\delta }_1}{n_2}\right)$

$n_1=1.00n_2=1.49\leftarrow Red1.53x0.98$

${\delta }_1=50{\delta }_2=30.72°$

$n_2=1.49n_3=1.00$

${\delta }_2=0.68°{\delta }_3=Si{n}^{-1}\left(\frac{n_{2}Sin{\delta }_2}{n_3}\right)$