Question

White light is incident onto a $30°$prism at the $40°$angle shown in $figurep35.41$. violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is $2.0\%$larger than the index of refraction of red light. At what angle does red light emerges from the rear face?

Short answer

The red light emerges from the rear face at angle$\sigma =1.02°$.

Step-by-step solution

Given information 

We need to find the angle of the red light emerges from the rear face.

Simplification 

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$

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

$n_1=1.00n_2=1.53\leftarrow videt1.50x1.02$

${\sigma }_1=50{\sigma }_2=30.04°$

Here, ${\sigma }_2$is the angle of deviation, role="math" localid="1650189647745" $n_{1}and{n}_2$are refractive index and ${\theta }_{1}and{\theta }_2$are the angle of incident.

localid="1650188923215" ${\sigma }_2={\sin }^{-1}\left(\frac{n_1\sin {\theta }_1}{n_2}\right)$

$n_1=1.00n_2=1.49\leftarrow red1.53x\sigma 98$

$\sigma =50{\sigma }_2=30.72°$

$$\begin{gathered} Red\sigma ={\sigma }_R-{\sigma }_V=30.72-30.04 \\ =0.68°. \end{gathered}$$

$n_2=1.49n_3=1.00$

${\sigma }_2=0.68°$

${\sigma }_3={\sin }^{-1}\left(\frac{n_2\sin {\sigma }_2}{n_3}\right)$

${\sigma }_3=1.02°$.

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