Question

Two monochromatic rays of light are incident normally on the face AB of a isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '1' and '2' are respectively 1.35 and 1.45. Trace the path of these rays after entering through the prism.

Answer 1

Critical angle is given by:

${\theta }_c={\sin }^{-1}\left(1/\mu \right)$

For ray 1,

$i={45}^o={sin}^{-1}\left(\frac{1}{1.414}\right)$

${\theta }_{c1}={sin}^{-1}\left(\frac{1}{1.35}\right)>{sin}^{-1}\left(\frac{1}{1.414}\right)$

Hence, ${\theta }_{c1}>i$

Ray will not undergo total internal reflection.

Applying snell's law,

$1.35sin\left(45\right)=1sin\left({\theta }_r\right)$

$sin\left({\theta }_r\right)=0.9545$

${\theta }_r\approx {72}^o$

For ray 2,

$i={45}^o={sin}^{-1}\left(\frac{1}{1.414}\right)$

${\theta }_{c2}=si{n}^{-1}\left(\frac{1}{1.45}\right)$

${\theta }_{c2}={sin}^{-1}\left(\frac{1}{1.45}\right)<{sin}^{-1}\left(\frac{1}{1.414}\right)$

Hence, ${\theta }_{c1}<i$

Ray will undergo total internal reflection.