Spherical mirrors

1.1 A visit to the science centre

Meena visited a science centre with her family and found a row of unusual curved mirrors. In one mirror her face looked unusually large, while her brother, standing farther away, looked upside down. Another mirror showed her a miniature self. She recalled the flat mirror she had used in Grade 7, which gives an erect image matching the object's size.

A guide explained that these were not plane mirrors but spherical mirrors. When a mirror is curved inward or outward, the image looks different. Meena decided to ask her teacher about these mirrors.

1.2 A spoon as a mirror

A shiny metallic spoon can act like a mirror. Bring the curved surface near your face and examine the inner side, which curves inward. The image of your face appears inverted. Now flip the spoon and look at the outer side, which bulges outward. The image is erect but smaller.

If you move the spoon away from your face while watching the image, the image changes. The spoon shows that a curved surface can form images very different from those of a flat mirror.

1.3 Concave and convex mirrors

Curved mirrors like the spoon can be specially made. A spherical mirror is shaped as a portion of an imaginary hollow glass sphere, and its reflecting surface is spherical. If the reflecting surface curves inward, the mirror is concave. If the reflecting surface curves outward, the mirror is convex.

The schematic representation of each mirror shows the non-reflecting surface as shaded. Such mirrors are not cut from a hollow glass sphere. A flat piece of glass is ground and polished into a curved surface, and a reflective coating such as a thin layer of aluminium is applied. A coating on the outer curved surface gives a concave mirror, while a coating on the inner curved surface gives a convex mirror.

1.4 Telling the two mirrors apart

Lay a concave and a convex mirror flat on a table, reflecting sides up, then view them from the side with your eye at their level. The reflecting surface of the concave mirror curves inward, while that of the convex mirror curves outward. The side view is usually enough to tell them apart.

1.5 Images in the two mirrors

Place an object a few centimetres in front of a concave and a convex mirror. With a concave mirror and a close object, the image appears erect and enlarged. As the object moves farther away, the image becomes inverted. It is enlarged at first and then keeps getting smaller.

A convex mirror, however, always shows an image that is erect and shrunk. The image shrinks a little more as the object is moved away. By contrast, a flat mirror always produces an erect image matching the object's size.

Lateral inversion appears in all three mirrors. The left and right sides of the object are swapped in the image, which is why writing appears reversed in a plane mirror.

The shape of the image therefore depends on the type of mirror and on the distance of the object from it. The mirror itself does not change; the geometry of the reflecting surface decides how the rays meet after reflection.

1.6 A plane mirror reminder

A flat mirror gives an erect image whose size equals the object's. The image appears to be behind the mirror, and it is laterally inverted, so writing looks reversed. These properties make the plane mirror a useful starting point for comparing curved mirrors.

In the science centre, Meena saw images that were larger, upside down, or tiny. None of these matches the plane mirror. The difference comes from the curvature of the reflecting surface, which changes the direction in which rays leave the mirror.

1.7 Curved surfaces and rays

Light travels from the object to the mirror in straight rays. At the mirror, each ray reflects according to the laws of reflection. On a flat mirror, all the normals point in the same direction, so a parallel beam stays parallel.

On a curved mirror, the normal points in a different direction at every point. The reflected rays therefore do not stay parallel: they may spread apart or come together. A convex mirror spreads the rays, and the eye traces them back to a smaller image. A concave mirror brings the rays together, which is why it can form an enlarged image when the object is close and an inverted image when the object is farther away.

1.8 Observing carefully

The activity with two mirrors and a small object is best done slowly. Note whether the image is erect or inverted, whether it is larger, smaller or the same size, and whether left and right are swapped. Then move the object back a little and repeat.

By comparing the observations for the concave mirror, the convex mirror and the plane mirror, the pattern becomes clear. The concave mirror is the only one that can form an inverted image of the object. The convex mirror is the only one whose image is always smaller and erect.