Question

A flint glass prism and a crown glass prism are to be combined in such a way that the deviation of the mean ray is zero. The refractive index of flint and crown glasses for the mean ray are 1.620 and 1.518 respectively. If the refracting angle of the flint prism is 6.0°, what would be the refracting angle of the crown prism?

Answer 1

If the refracting angle of the flint prism is 6.0°, what would be the refracting angle of the crown prism is 7.18°.

Explanation:

Given data in the question  :      

The refractive index for the mean radius of flint and crown glasses is 1,620 and 1,518 respectively

(i.e )

Flint glass Refractive index is  $\begin{equation}=\mathrm{u}_{\mathrm{f}}=1.620\end$

Crown glass Refractive index is $\begin{equation}=\mathrm{u}_{\mathrm{c}}=1.518\end$

Flint prism refracting  angle is $\begin{equation}=\mathrm{A}_{\mathrm{f}}=6.0^{\circ}\end$

We know that,  

The crown prism refracting angle,  

$\begin{equation}\left(u_{f}-1\right) A_{f}=\left(u_{c}-1\right) A_{c}\end$

$\begin{equation}\frac{\left(\mathrm{u}_{\mathrm{f}}-1\right) \mathrm{A}_{\mathrm{f}}}{\left(\mathrm{u}_{\mathrm{c}}-1\right)}=\mathrm{A}_{\mathrm{c}}\end$

$\begin{equation}A_{c}=\frac{(1.620-1) \mathrm{A}_{\mathrm{f}}}{(1.518-1)}\end$

$\begin{equation}A_{c}=\frac{(0.62) 6.0}{(0.518)}\end$

$\begin{equation}A_{c}=1.196 \times 6.0^{\circ}\end$

$\begin{equation}A_{c}=7.18^{\circ}\end$

Thus, the crown prism refracting angle is 7.18° .