Name: Normal Incidence of Light Ray
Uploaded: 2019-07-19
Duration: 4 min 35 s
Description: When a light ray falls on a glass slab, the way it is refracted depends on the ray that is incident on the glass slab. Watch the video to learn more about it.

Question

Determine the focal length of a concave spherical mirror which is manufactured in the form of a thin symmetric biconvex glass lens

(η = 1.5)

one of whose surfaces is silvered. The curvature radius of the lens surface is

R = 40 cm

.

Accepted Answer

When a lens is silvered, then the system is equivalent to a combination of a lens, a mirror and a lens.

Power $P$ the system is given by,

$P = P_{L} + P_{M} + P_{L} \Rightarrow P = 2 P_{L} + P_{M} . . . (1)$

where $P_{L}$ and $P_{M}$ are the power of lens and mirror, respectively.

Now, let us determine the focal lengths and hence, the powers of the thin lens and silvered surface separately.

The focal length of the thin lens in air is given by,

$\frac{1}{f_{L}} = (n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$ .

Given, $R_{1} = + R, R_{2} = - R, n = \frac{3}{2}, R = 40 cm$

$∴ \frac{1}{f_{L}} = (n - 1) \frac{2}{R}$ .

Hence, the power of the lens is,

$P_{L} = \frac{1}{f_{L}} = \frac{2 (n - 1)}{R} . . . (2)$

Now, the focal length of the concave mirror is given by,

$f_{M} =$ $- \frac{R}{2}$ .

Hence, the power of the mirror is given by,

$P_{M} = - \frac{1}{f_{M}} = \frac{2}{R} . . . (3)$

Hence, the power of the combination is given by the equation $(1)$ ,

$∵ P = 2 P_{L} + P_{M}$

$\Rightarrow P = \frac{4 (n - 1)}{R} + \frac{2}{R}$ [using the equations $(2) & (3)]$

$∴ P = (\frac{4 n - 2}{R})$

As the power of the equivalent mirror is,

$P = - \frac{1}{F}$ ,

where $F$ is the focal length of the equivalent mirror.

$∴ F = - \frac{1}{P} = - \frac{R}{4 n - 2} \Rightarrow F = - \frac{R}{2 (2 n - 1)}$

Putting $R = 40 cm$ and $n = \frac{3}{2}$ , we get,

$F = - \frac{40}{2 (2 \times \frac{3}{2} - 1)}$

$\Rightarrow F = - 10 cm$

Hence, the equivalent system is a concave mirror of focal length $10 cm$ .

Determine the focal length of a concave spherical mirror which is manufactured in the form of a thin symmetric biconvex glass lens $(η = 1.5)$ one of whose surfaces is silvered. The curvature radius of the lens surface is $R = 40 cm$ .

Important Questions on OPTICS

Learn and Prepare for any exam you want !

Determine the focal length of a concave spherical mirror which is manufactured in the form of a thin symmetric biconvex glass lens ( η=1.5) one of whose surfaces is silvered. The curvature radius of the lens surface is R=40 cm.

Important Questions on OPTICS

Learn and Prepare for any exam you want !

Determine the focal length of a concave spherical mirror which is manufactured in the form of a thin symmetric biconvex glass lens $(η = 1.5)$ one of whose surfaces is silvered. The curvature radius of the lens surface is $R = 40 cm$ .