Question

The diagram alongside shows the refraction of a ray of light from air to liquid.

$\left(a\right)$ Write the values of $\left(i\right)$ angle of incidence, and $\left(ii\right)$ angle of refraction.

$\left(b\right)$ Use Snell's law to find the refractive index of liquid with respect to air

Answer 1

Angle of Incidence $=i$,

Angle of Refraction $=r$

Normal makes ${90}^{\circ }$ angle with the surface.

$\angle i={90}^{\circ }-{30}^{\circ }={60}^{\circ }$

$\angle r={90}^{\circ }-{45}^{\circ }={45}^{\circ }$



The ratio of the sine of the angle of incidence $\left(i\right)$ to the sine of the angle of refraction $\left(r\right)$ is constant for the pair of given media.

$\frac{\sin i}{\sin r}=\mu$

Where $\mu$ is refractive index of liquid with respect to air.

$\angle i={90}^{\circ }-{30}^{\circ }={60}^{\circ }$

$\angle r={90}^{\circ }-{45}^{\circ }={45}^{\circ }$

Now, $\frac{\sin 60}{\sin 45}=\mu$

$\mu =\frac{\sqrt{3}\times \sqrt{2}}{2\times 1}=\sqrt{\frac{3}{2}}=1.22$