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# Spherical Mirrors - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

## Quick Facts

• Spherical mirrors is considered one of the most asked concept.

• 9 Questions around this concept.

## Solve by difficulty

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface.  A small air bubble is 6 cm below the flat surface inside it along the axis.  The position of the image of the air bubble made by the mirror is seen :

You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :

A real image of half the size is obtained in a concave spherical mirror with a radius of curvature of 40 cm. The distance of the object and that of its image from the mirror will be respectively :

A spherical mirror forms a diminished virtual image of magnification $1/3$ and the Focal length is $\mathrm{18\ cm}$. The distance of the object is:

Consider the situation as shown in figure. The point $\mathrm{O}$ is the centre. The light ray forms an angle of $\mathrm{60^{\circ}}$ with the normal. The normal makes an angle $\mathrm{60^{\circ}}$ with the horizontal and the mirror makes an angle $\mathrm{60^{\circ}}$ with the normal. The value of refractive index of that spherical portions, so that light ray retraces its path is:

## Concepts Covered - 1

Spherical mirrors

Spherical mirror-

It is a part of a transparent hollow sphere whose one surface is polished.

There are two types of spherical mirrors: concave, and convex.

In the above figure, A concave (left) and a convex (right) mirror is shown.

Some important terminology-

• Centre of curvature (C)- The Centre of the sphere of which the mirror is a part is called Centre of curvature.
• Pole (P)- The geometrical centre of the spherical reflecting surface.
• The radius of curvature (R)- The radius of the sphere of which the mirror is a part is called the radius of curvature.

or R=Distance between pole and centre of curvature

$\left( Note \ \ \Rightarrow \ \ R_{\text {concave }}=-v e, \quad R_{\text {convex }}=+v e, R_{\text {plane }}=\infty\right)$

• Principle axis- A line passing through P and C is known as the Principle axis.
• Focus (F)- When a narrow beam of rays of light, parallel to the principal axis and close to it, is incident on the surface of a mirror, the reflected beam is found to coverage to or appears to diverge from a point on the principal axis. This point is called the focus.

or  An image point on the principal axis for which object is at $\infty$ is called the focus.

C, P, F for a concave mirror are shown in the below figure.

• Focal Length (f)- It is the distance between the pole and the principal focus. For spherical mirrors, $f=\frac{R}{2}$

$\left(i.e \ \ f_{\text {concare }}=-v e, f_{\text {convex }}=+v e, f_{\text {plane }}=\infty\right)$

• Focal plane- A plane passing from focus and perpendicular to the principal axis.

## Study it with Videos

Spherical mirrors

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