Chapter 23, Problem 14P

The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 19.0 cm behind the mirror. What kind of mirror is it, and what is its radius of curvature?

To determine

The nature of mirror and calculate its radius of curvature.

Answer to Problem 14P

Solution:

The nature of mirror is convex mirror as focal length is negative and its radius of curvature will be 38.0 cm.:

Explanation of Solution

Given Info:

Image distance ‘v’= – 19.0 cm

Nature of image is virtual and very small

Object distance ‘u’ = infinity

Let the focal length of mirror be ‘f’

Formula Used:

Apply focal length formula for mirror

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

Here, all alphabets are in their usual meanings.

Calculation:

Sine the nature of image is virtual and very small then given mirror must be convex mirror.

Apply focal length formula for mirror

$\begin{array}{l}\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\ \frac{1}{f}=\frac{1}{-19.0cm}+\frac{1}{\infty }\\ f=-19.0cm\end{array}$

Since the radius of curvature R = 2f

So, the radius of curvature R = 2 x (– 19.0 cm)= – 38.0 cm: