Question

The referacting angles of the flint and crown glass prisms are $A^{\prime }$ and $A$ and their refractive indices are ${\mu }^{\prime }$ and $\mu$ respectively. They are to be used for dispersion without deviation. The ratio of their referacting angles $\frac{A^{\prime }}{A}$ will be :

• A. $\frac{A^{\prime }}{A}=\left(\frac{1+\mu }{{\mu }^{\prime }-1}\right)$
• B. $\frac{A^{\prime }}{A}=\left(\frac{1-\mu }{{\mu }^{\prime }-1}\right)$
• C. $\frac{A^{\prime }}{A}=\left(\frac{1-\mu }{{\mu }^{\prime }+1}\right)$
• D. $\frac{A^{\prime }}{A}=\left(\frac{1-\mu }{1-{\mu }^{\prime }}\right)$

Answer 1

The correct option is B $\frac{A^{\prime }}{A}=\left(\frac{1-\mu }{{\mu }^{\prime }-1}\right)$

We know that, for dispersion without deviation :

$\text{Angle of deviation due to prism 1}$
$\text{+ Angle of deviation due to prism}2=0$

$\Rightarrow {\delta }_1+{\delta }_2=0$

$\Rightarrow A(\mu -1)+A^{\prime }({\mu }^{\prime }-1)=0$

$\Rightarrow \frac{A^{\prime }}{A}=\left(\frac{1-\mu }{{\mu }^{\prime }-1}\right)$

Thus, option $\left(b\right)$ is the correct answer.