Physics - Geometrical Optics Question with Solution | TestHub

Speed of light in air is given by $v_1=\frac{x}{t_0}$

Speed of light in the denser medium is given by $v_2=\frac{4x}{t_1}$

The refractive index of the denser medium with respect to air is $\mu =\frac{v_1}{v_2}$

The critical angle ${\theta }_c$ for the medium is given by $\sin {\theta }_c=\frac{1}{\mu }=\frac{v_2}{v_1}$

Substituting the values of $v_1$ and $v_2$:

$\sin {\theta }_c=\frac{\frac{4x}{t_1}}{\frac{x}{t_0}}=\frac{4t_0}{t_1}$

${\theta }_c={\sin }^{-1}\left(\frac{4t_0}{t_1}\right)$

Answer: ${\sin }^{-1}\left(\frac{4t_0}{t_1}\right)$