Question

The diagram alongside shows the refraction of a ray of light from air to a liquid. The refractive index of liquid with respect to air is :

• A. $\sqrt{\frac{1}{{}_2}}$
• B. $\sqrt{\frac{2}{{}_3}}$
• C. $\sqrt{\frac{3}{{}_2}}$
• D. $\sqrt{3}$

Answer 1

The correct option is C $\sqrt{\frac{3}{{}_2}}$

According to Snell's law when light goes from rarer to denser medium ,

$n_2\sin r=n_1\sin i$ ...............$\left(1\right)$

where, $n_2$ is refractive index of denser medium(liquid), $n_1$ is refractive index of rarer medium(air).

Angle of incidence with the normal(dashed line in the figure ) = $i$

Angle of refraction with the normal = $r$

According to the given figure, $i={60}^o$ and $r={45}^o$

Define $n=\frac{n_2}{n_1}$ , which is refractive index of liquid with respect to air.

Using equation $\left(1\right)$ we get,

$n=\frac{\sin {60}^o}{\sin {45}^o}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}}}$
$n=\sqrt{\frac{3}{2}}$

Option C is correct.