Question

(a) State Snell's law for refraction of light.
(b) A concave mirror forms two times magnified and real image of an object placed at $15cm$ from its pole. Determine the distance of the image from the mirror and the focal length of the mirror.

Answer 1

(a) The ratio of the sine of angle of incidence to the sine of angle of refraction is a constant for the light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction of light.

Mathematically, $\frac{n_2}{n_1}=\frac{\sin i}{\sin r}$

where, $i$ is the angle of incidence, $r$ is the angle of refraction, $n_1$ and $n_2$ are the refractive indices of medium 1 and 2 respectively.

(b) Given:

object diatance $u=-15cm$

magnification $m=-2$

$v=?,f=?$

Using the formula of magnification we can write,

$m=\frac{-v}{u}$

$\Rightarrow -2=\frac{-v}{-15}$

$\Rightarrow v=-30cm$

Therefore, distance of image from the mirror, $v=-30cm$

Again from the mirror formula we can write,

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{f}=\frac{1}{-30}+\frac{1}{-15}$

Focal length, $f=\frac{(-15)\times (-30)}{(-15)+(-30)}=-10cm$