Question

(a) Write the relation between object distance $\left(u\right)$, image distance $\left(v\right)$ and focal distance $\left(f\right)$ of a spherical lens.

(b) What is magnification?
(c) The refractive index of glass with respect to air is $\frac{3}{2}$ and the refractive index of water with respect to air is $\frac{4}{3}$. If the speed of light in air is $3\times {10}^{8}m/s$, find the speed of light in (i) glass, (ii) water.

Answer 1

(a) The relation between object distance $\left(u\right)$, image distance $\left(v\right)$ and focal distance $\left(f\right)$ of a spherical lens:

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

(b) Magnification is defined as the ratio of the height of the image to the height of the object.

Magnification, $m=\frac{h_i}{h_o}$

(c) Given:

The refractive index of glass with respect to air = $\frac{3}{2}$

The refractive index of water with respect to air = $\frac{4}{3}$

Refractive index (of a medium) $=\frac{speedoflightinair}{speedoflightinmedium}$

(i) $\frac{3}{2}=\frac{speedoflightinair}{speedoflightinglass}$

Speed of light in glass = $\frac{speedoflightinair}{1.5}$ = $\frac{3\times {10}^8}{1.5}=2\times {10}^{8}m/s$

(ii) $\frac{4}{3}=\frac{speedoflightinair}{speedoflightinwater}$

Speed of light in water = $\frac{speedoflightinair}{1.33}$ = $\frac{3\times {10}^8}{1.33}=2.25\times {10}^{8}m/s$