Chapter 23, Problem 21P

To determine

Part (a) To Determine:

About the type of mirror.

Answer to Problem 21P

Solution:

The nature of the mirror will be concave:

Explanation of Solution

Given Info:

Magnification of the mirror ‘m’ = +1.40

Object distance $u=+20.0cm$

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

Let the image distance be ‘v’

Let the focal length of mirror be ‘f’

Formula Used:

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

Here, all alphabets are in their usual meanings.

Calculation:

Since the magnification of the mirror is positive. Hence the given mirror will be concave:

To determine

Part (b) To Determine:

The nature of the image.

Answer to Problem 21P

Solution:

The nature of the image will be upright, magnified, virtual and formed behind the mirror.:

Explanation of Solution

Given Info:

Magnification of the mirror ‘m’ = +1.40

Object distance $u=+20.0cm$

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

Let the image distance be ‘v’

Let the focal length of mirror be ‘f’

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 magnification of mirror $m=-\frac{v}{u}$

$\begin{array}{l}+1.40=-\frac{v}{+20.0cm}\\ v=-28.0cm-------(i)\end{array}$

Again, apply magnification of mirror $m=\frac{h_i}{h_0}$

$\begin{array}{l}+1.40=\frac{h_i}{h_0}\\ or,h_i=1.4h_0--------(ii)\end{array}$

From equation (i)and (ii), we can conclude that the image will be upright, magnified, virtual and formed behind the mirror.:

To determine

Part (c) To Determine:

The radius of the curvature of the mirror.

Answer to Problem 21P

Solution:

The radius of the curvature of the mirror will be 1.4 m.

Explanation of Solution

Given Info:

Magnification of the mirror ‘m’ = +1.40

Object distance $u=+20.0cm$

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

Let the image distance be ‘v’

Let the focal length of mirror be ‘f’

Formula Used:

(i)Apply focal length formula for mirror

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

Here, all alphabets are in their usual meanings.

Calculation:

Apply focal length formula for mirror

$\begin{array}{l}\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\ \frac{1}{f}=\frac{1}{-28.0cm}+\frac{1}{+20.0cm}\\ f=+70.0cm\end{array}$

Since the radius of curvature R = 2f

So, the radius of curvature R = 2 ?— (+70.0 cm)= + 1.4 m