Physics - Geometrical Optics Question with Solution | TestHub

By Snell's law, $\sin i=\mu \sin r$, which gives $\sin r=\frac{\sin i}{\mu }$.

The distance travelled by the ray inside the glass slab is $d=\frac{t}{\cos r}$.

The speed of light inside the glass slab is $v=\frac{c}{\mu }$.

The total time spent by the ray inside the slab is $T=\frac{d}{v}=\frac{t}{\cos r}\times \frac{\mu }{c}=\frac{\mu t}{c\cos r}$.

Using $\cos r=\sqrt{1-{\sin }^{2}r}=\sqrt{1-\frac{{\sin }^{2}i}{{\mu }^2}}=\frac{\sqrt{{\mu }^2-{\sin }^{2}i}}{\mu }$.

Substituting $\cos r$ in the expression for $T$, we get $T=\frac{\mu t}{c\left(\frac{\sqrt{{\mu }^2-{\sin }^{2}i}}{\mu }\right)}=\frac{{\mu }^{2}t}{c\sqrt{{\mu }^2-{\sin }^{2}i}}$.

Answer: $\frac{{\mu }^{2}t}{c\sqrt{{\mu }^2-{\sin }^{2}i}}$