A beam of light is incident from air on the surface of a liquid. The angle of incidence is $ heta$ and the angle of refraction is $\alpha$. If the critical angle for liquid when surrounded by air is $ heta_c$ then $\sin heta_c$ is

Question

A beam of light is incident from air on the surface of a liquid. The angle of incidence is $	heta$ and the angle of refraction is $\alpha$. If the critical angle for liquid when surrounded by air is $	heta_c$ then $\sin 	heta_c$ is

Aicharya · Accepted Answer

Refractive index of liquid with respect to air, $n_{l a}=\frac{\sin i}{\sin r}$ Here, $i=\theta$ and $r=\alpha$

So, refractive index of liquid with respect to air, $n_{l a}=\frac{\sin \theta}{\sin \alpha}$ Now, if $\theta_c=$ angle of critical incidence for liquid then,

refractive index of air with respect to liquid is $n_{a l}=\frac{1}{n_{l a}}=\frac{\sin \theta_c}{\sin 90^{\circ}}$ $\Rightarrow \sin \theta_c=\frac{1}{n_{l a}}=\frac{\sin \alpha}{\sin \theta}$

A beam of light is incident from air on the surface of a liquid. The angle of incidence is $\theta$ and the…

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