**SPHERICAL MIRRORS**

Spherical mirrors are generally constructed from glass. One surface of the glass is silvered. The reflection takes place at the other surface. If reflection takes place at the convex surface (figure 3b), it is called a * convex mirror* and if reflection takes place at the concave surface (figure 3a), it is called a

*. Some common examples of concave mirrors are shaving mirrors and makeup mirrors. These types of mirrors magnify objects placed close to them. A common example of convex mirrors is the passenger-side wing mirrors of cars. These type of mirrors have wider fields of view than equivalent flat mirrors, but objects which appear in them generally look smaller (and, therefore, farther away) than they actually are.*

**concave mirror****Some definitions regarding spherical mirrors**

- The centre of the sphere, of which the mirror is a part, is called the
of the mirror (Point C in figure 3).*centre of curvature* - The radius of this sphere is called the
of the mirror (length of CP in figure 3).*radius of curvature* - The line joining the pole and the centre of curvature is called the
(Straight line PC in figure 3).*principal axis* - Suppose a light beam travelling in a direction parallel to the principal axis is incident on a concave mirror. The point where the reflected rays converge is called the
of the mirror (Point F in figure 3a). In case of a convex mirror, the reflected rays appear to diverge from a point on the principal axis (Point F in figure 3b). This point is the focus of the convex mirror.*focus* - The plane through the focus and perpendicular to the principal axis is called the
.*focal plane* - The distance of the focus from the pole is called the
of the mirror (length of FP in figure 3).*focal length* - A ray close to the principal axis is called a
.*paraxial ray*

**Real and virtual images**

When a point object is placed before a spherical mirror of small aperture, a point image is formed. A reflected ray is traced by applying the laws of reflection. If the reflected rays intersect, the point of intersection is the * real image*. If the rays diverge after reflection,

*is formed at the point from where the rays seem to diverge. Figure 4 shows some examples.*

**a virtual image****Sign Convention**

In the sign convention for spherical mirrors, the pole^{1} is taken to be the origin and the principal axis as the x-axis. The quantities *u*, *v*,* R* and* f* denote the x-coordinates of the object, the image, the centre of curvature and the focus respectively. The sign convention for spherical mirrors is summarised in table 1.

It can be proved that the quantities *u*, *v* and* R* are related through the relation

**Extended Objects and Magnification**

Suppose an object *AB* is placed on the principal axis of a spherical mirror with the length *AB* perpendicular to the principal axis (figure 5a). Consider two rays *BD* and *BE*, the first parallel to the principal axis and the other directed towards the centre of curvature. The image of *B* is formed at the intersection of these two reflected rays. Thus,* A’B’* is the image of *AB*. The * lateral or transverse magnification* is defined as

where h_{2} = height of the image and h_{1} = height of the object. The height of the object (placed perpendicular to the principal axis) is taken to be positive. If the image is also on the same side of the principal axis, its height is also positive. The image is then erect. If the image is inverted, its height is taken as negative. Figure 5b shows an example of inverted image. It can be shown that the lateral magnification of an extended object by a spherical mirror

** Further reading**

### Beginner level:

1. This video shows reflection of a parallel light beam from a concave mirror –

2. This video shows reflection of a parallel light beam from a convex mirror –

### Advanced level:

1. This website illustrates different cases of image formation by spherical mirrors: http://dev.physicslab.org/Document.aspx?doctype=3&filename=GeometricOptics_SphericalMirrors.xml

^{1} The point on the mirror at the middle of the surface is called its ** pole** (Point P in figure 3).

**MCQs on SPHERICAL MIRRORS**

**Question 01**

A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm. The image will form at

**Options:**

- infinity
- pole
- focus
- 15 cm behind the mirror.

**Question 02:**

The image formed by a convex mirror of a real object is

**Options:**

- virtual and erect
- virtual and inverted
- real and erect
- real and inverted

**Question 03:**

A virtual image larger than the object can be produced by

**Options:**

- concave mirror
- convex mirror
- plane mirror
- concave lens

**Question 04:**

In image formation from spherical mirrors, only paraxial rays are considered because they

**Options:**

- are easy to handle geometrically
- contain most of the intensity of the incident light
- form nearly a point image of a point source
- show minimum dispersion effect.

**Question 05:**

Which of the following (referred to a spherical mirror) depends on whether the rays are paraxial or not?

**Options:**

- Pole
- Focus
- Radius of curvature
- Principal axis

**Correct Answers:**

Question 01: D

Question 02: A

Question 03: A

Question 04: C

Question 05: B