Question

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$, a ray incident at an angle $\theta$, on the face AB would get transmitted through the face AC of the prism, provided

• A. $\theta >si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
• B. $\theta <si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
• C. $\theta >co{s}^{-1}\left[\mu sin(A+si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$
• D. $\theta <co{s}^{-1}\left[\mu sin(A+si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$

Answer 1

The correct option is A $\theta >si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))\right]$

At face AB,
$sin\theta =\mu sinr$
At face Ac,
$r^{\prime }<{\theta }_C$
$\Rightarrow A-r<si{n}^{-1}\left(\frac{1}{\mu }\right)$
$\Rightarrow r>A-si{n}^{-1}\left(\frac{1}{\mu }\right)$
$\Rightarrow sinr>sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))$
$\Rightarrow \frac{sin\theta }{\mu }>sin(A-si{n}^{-1}\left(\frac{1}{\mu }\right))$
$\therefore \theta >si{n}^{-1}\left[\mu sin(A-si{n}^{-1}\frac{1}{\mu })\right]$