Chapter 17, Problem 47A

To determine

The location of the object if it produces a virtual image in a concave mirror.

Answer to Problem 47A

In between the mirror and its focus point in front of the mirror.

Explanation of Solution

Introduction:

Mirror equation,

  $\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$

Where,

  $\begin{array}{l}f=\text{focal length}\\ d_i=\text{ image distance}\\ d_o=\text{object distance}\end{array}$

A concave mirror always produced a real and an inverted image of an object except for the case when the object distance is less than the focal length. For this case, the image distance comes out to be negative, that is the image is formed behind the mirror or the image is a virtual one.

  $\frac{1}{d_i}=\frac{1}{f}-\frac{1}{d_o}$

If $d_o<f$ , then $d_i$ will be negative, thus a virtual image is formed behind the mirror.

Conclusion:

Hence, if the object is located in between the concave mirror and its focus, the image produced by it will be virtual.