Question

A glass prism with the refracting angle of $60°$and refractive index of $1.5$ is completely immersed in water with a refractive index $1.33$. Calculate the angle of minimum deviation of the prism in this situation,${\sin }^{-1}\left(0.56\right)=34.3°$.

Answer 1

Step 1: Given data

The angle of the prism, $A$$=60°$

Refractive index of the glass prism $=1.5$

Refractive index of water $=1.33$

Step 2: Calculating the angle of minimum deviation

Now, the refractive index of the prism with respect to the water, $\mu =\frac{1.5}{1.33}=1.127$

Condition for minimum deviation,

$\mu =\frac{\sin \left({\displaystyle \frac{A+{\delta }_n}{2}}\right)}{\sin {\displaystyle \frac{A}{2}}}$

Here,

$$\begin{gathered} {\delta }_n=minimumangleofrefraction \\ A=Angleofprism \end{gathered}$$

$$\begin{gathered} \Rightarrow 1.127=\frac{\sin \left({\displaystyle \frac{60°+{\delta }_n}{2}}\right)}{\sin (30°)} \\ \Rightarrow 0.56=\sin \left(\frac{60°+{\delta }_n}{2}\right) \\ \Rightarrow 68.6°=60°+{\delta }_n \\ \Rightarrow {\delta }_n=8.6° \end{gathered}$$

Hence, the angle of minimum deviation is $8.6°$.