Chapter 17, Problem 83A

To determine

Type of spherical mirror used.

Answer to Problem 83A

The spherical mirror used is concave mirror.

Explanation of Solution

Given:

The ball position both mirror is 22 cm in front of mirror. So, $u=-22\text{cm}$

The image appears 12 cm closer if spherical mirror is replaced with a plane mirror.

Formula Used:

The lens formula is given as,

  $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Here, $f$ is focal length of spherical mirror, $v$ is image position and $u$ is object position.

Calculation:

Since, for plane mirror object distance is $u=-22\text{cm}$

As the image formed by plane mirror is virtual so, $v=22\text{cm}$

Now, on replacing spherical mirror with plane mirror the image appears 12 cm closer.

So, the image distance for spherical mirror is,

  $\begin{array}{l}v=22+12\\ =34\text{cm}\end{array}$

Now putting $u=-22\text{cm}$ and $v=34\text{cm}$ in the lens formula

  $\begin{array}{l}\frac{1}{f}=\frac{1}{34}+\frac{1}{-22}\\ =\frac{-22+34}{34\times \left(-22\right)}\\ \Rightarrow f=\frac{-748}{12}=-62.33\text{cm}\end{array}$

Since, f is negative which means the spherical mirror used is concave mirror.

Conclusion:

Therefore, the spherical mirror used is concave mirror.