Chapter 23, Problem 4Q

To determine

Whether the image formed is real or virtual, inverted or upright, the mirror is concave or convex, the side in which the image is located if the magnification of the object is given as -2.0.

Answer to Problem 4Q

Solution:

The image is real and inverted. The mirror is concave. The image is on the same side of the object.

Explanation of Solution

An object is placed along the principle axis of a spherical mirror.

Given:

The magnification of the object is m = -2.0

Formula used:

The magnification of a spherical mirror is given by

$magnification\text{ of mirror m =}\left(\text{-}\frac{\text{image distance}}{\text{ object distance}}\right)$

Calculation:

The magnification is negative (-2.0):

If m is negative then the image formed by the spherical mirror is a real and inverted image.

The concave spherical mirror:

gives only a real and inverted image, however, it can give a virtual image also depending on the object’s position. But, the convex mirror gives only virtual image.

As the image formed here is a real image, it is formed by the concave mirror.

As m is -2.0, then the image distance and the object distance are positive:

If both the image and the object distance are positive, object and the image are situated in front of the mirror. Both are on the same side.