Question

An object is kept at a distance of $4m$ in front of a spherical mirror which forms its erect image at a distance of$1.0m$ from the mirror. What is the magnification? Is the mirror concave or convex?

Answer 1

Step 1 - Given data

The distance of the object from the pole of the mirror $u=-4m$ (The negative sign indicates that the object is placed in front of the mirror.)

The distance of the image from the pole of the mirror $v=1.0m$ (The erect image is formed behind the mirror. )

Step 2 - Finding the magnification

The magnification $\left(m\right)$ can be calculated as

$$\begin{gathered} m=-\frac{v}{u} \\ m=-\frac{(1m)}{(-4m)} \\ m=+\frac{1}{4} \end{gathered}$$

Step 3 - The type of mirror

• The magnification is positive, hence the image formed is virtual.
• A concave mirror forms a virtual magnified image. That means the magnification value is greater than 1.
• The magnification of the convex mirror is always less than 1.
• In this case, the magnification is between 0 and 1. Therefore the mirror used is a convex mirror.

Final answer - Hence, the magnification is $+\frac{1}{4}$ and the mirror is a convex mirror.