Question

List the sign conventions for reflection of light by spherical mirrors. Draw a diagram and apply these conventions in the determination of focal length of a spherical mirror which forms a three times magnified real image of an object placed 16 cm in front of it.
OR
State the law of refraction of light that defines the refractive index of a medium with respect to the other. Express it mathematically. How is refractive index of any medium 'A' with respect to a medium 'B' related to the speed of propagation of light in two media A and B? State the name of this constant when one medium is vacuum or air.

The refractive indices of glass and water with respect to vacuum are $\frac{3}{2}$ and $\frac{4}{3}$ respectively. If the speed of light in glass is $2\times {10}^{8}m/s$, find the speed of light in (i) vacuum, (ii) water.

Answer 1

Sign conventions for spherical mirrors

I.Objects are always placed to the left of the mirror i.e. light must fall on the mirror from left to right.

II.All distances are measured from the pole of the mirror.

III.Distances along the direction of the incident ray (along positive X-axis) are taken as positive.

IV.Heights measured perpendicular to and above the principal axis (along positive Y-axis) are taken as positive.

V.Heights measured perpendicular to and below the principal axis (along negative Y-axis) are taken as negative.

Given,
m = -3 (real image is inverted always)
u=-16 cm
Now,
$m=-\frac{v}{u}=-\frac{v}{(-16)}=\frac{v}{16}-3=\frac{v}{16}$
v=-48cm
Using mirror formula,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\frac{1}{f}=\frac{1}{(-48)}+\frac{1}{(-16)}=-\frac{1}{12}f=-12cm$
OR
The law of refraction that defines the refractive index of a medium with respect to the other is given by first law of refraction known as Snell's law.
First law of refraction
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
This is known as Snell's law. Mathematically, it can be given as follows:
$\frac{sini}{sinr}=constant{=}^a{\mu }_b$
Here, ${}^a{\mu }_b$ is the relative refractive index of medium b with respect to medium a. consider a ray of light travelling from medium B into medium A. let $v_1$ be the speed of light in medium A and $v_2$ be the speed of light in medium B. then the refractive index of medium A with respect to medium B is given by
$n_{AB}=\frac{v_2}{v_1}$
If one medium is vacuum or air then the constant is named as absolute refractive index of the medium.
Let, absolute refractive index of glass, $n_g=\frac{3}{2}$
Absolute refractive index of water, $n_w=\frac{4}{3}$
Speed of light in glass, $v_g={2.10}^{8}m/s$
(i) Speed of light in vacuum
$n_g=\frac{c}{v_g}c=n_g\times v_g=\frac{3}{2}\times 2\times {10}^{8}m/s$
(ii) Speed of light in water,
$n_w=\frac{c}{v_w}{v}_w=\frac{c}{n_w}=\frac{3\times {10}^8}{\left(\frac{4}{3}\right)}=2.25\times {10}^{8}m/s$