Chapter 23, Problem 18Q

To determine

The type of mirror in the given figure.

Answer to Problem 18Q

Solution:

The mirror in the given figure is concave. The person is standing very close to the mirror, which means within the focal length of the mirror and he sees his image,which is an upright and larger virtual image formed behind the mirror. The image of that kind will be given by aconcave mirror.

Explanation of Solution

The concave mirror produces the virtual image and also upright behind the mirror, when the object is placed within the focal length of the mirror, between the center of the mirror and the focal point. This is depicted by the ray diagram as follows.

The man is standing very close to the mirror, which is having a big curvature. As he is very close, he is standing within the focal point of the mirror,the man is between the mirror andthe focal point.

Three rays are considered to describe the image formation.

Ray 1 leaves the tip of man, heading toward the mirror parallel to the axis, and reflects through F.

Ray 2cannot head toward F because it would not strike the mirror; so ray 2 must point as if it started at F (dashed line)and heads to the mirror, andthen is reflected parallel to the principal axis.

Ray 3 is perpendicular to themirror and reflects back on itself. The rays reflected from the mirror diverge andso never meet at a point.

All of the reflected rays appear to be coming from a point behind themirror (dashed lines).This point locates the image of the man. The image is thus behind the mirror and is virtual and upright.