Question

A short straight object of height $100cm$ lies before the central axis of a spherical mirror whose focal length has absolute value$\left|f\right|=40cm$. The image of the object produced by the mirror is of height $25cm$ and has the same orientation as the object. One may conclude from the information:

• A. Image is real, same side of concave mirror
• B. Image is virtual, opposite side of convex mirror.
• C. Image is virtual, opposite side of concave mirror.
• D. Image is real, same side of convex mirror.

Answer 1

The correct option is B

Image is virtual, opposite side of convex mirror.

Step 1. Given data

The height of the short straight object is $H=100cm$

The focal length of a spherical mirror is $\left|f\right|=40cm$

The height of the image object is $I=25cm$

Step 2. By using the magnification formula

We know that the magnification formula is given by $M=\frac{I}{H}$

Where, $M$ is the magnification of the mirror

$I$ is the height of the image

$H$ is the height of the object

By substituting the given values in the formula we get,

$\begin{array}{rcl}M& =& \frac{25}{100}\\ & =& \frac{1}{4}\\ & =& 0.25\end{array}$

Since the magnitude of magnification is positive then it indicates that the image is virtual, therefore mirror can be concave or convex. However, the magnitude of magnification is $<1$, which means the image size is smaller than object this can only happen with a convex mirror, not with a concave mirror.

Therefore, the correct option is (B).