Chapter 23, Problem 17P

To determine

The image distance and its characteristics.

Answer to Problem 17P

Solution:

The image is formed at 2.0 cm behind the tree ball. It will be upright, virtual and smaller than the object’s height.

Explanation of Solution

Given Info:

Image is upright.

Let height of object be $+h_0$ and height of image be $h_i$

Object distance $u=+25.0\text{cm}$

Radius of curvature R = – 4.4 cm

Focal length of convex mirror f = – 2.2 cm

Let image distance be ‘v’

Formula Used:

(i)Apply focal length formula for mirror

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

(ii)Magnification of mirror $m=\frac{h_i}{h_0}=-\frac{v}{u}$

Here, all alphabets are in their usual meanings.

Calculation:

Apply focal length formula for mirror

$\begin{array}{l}\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\ \frac{\text{1}}{\text{-2}\text{.2 cm}}=\frac{1}{v}+\frac{\text{1}}{\text{+25}\text{.0 cm}}\\ or,v=-\text{2}\text{.0}\text{cm}\end{array}$

Apply magnification of mirror

$m=\frac{h_i}{h_0}=-\frac{v}{u}$

$\begin{array}{l}\frac{h_i}{h_0}=-\frac{\text{-2}\text{.0 cm}}{\text{+25}\text{.0 cm}}\\ h_i=+\frac{2}{25}{h}_o\end{array}$

Hence the image is formed at 2.0 cm behind the tree ball. It will be upright, virtual and smaller the object’s height.