Chapter 23, Problem 10P

A small candle is 38 cm from a concave mirror having a radius of curvature of 24 cm. (a) What is the focal length of the mirror? (b) Where will the image of the candle be located? (c) Will the image be upright or inverted?

To determine

(a) To determine:

What is the focal length of the mirror?

Answer to Problem 10P

Solution:

Focal length of concave mirror is -12 cm

Explanation of Solution

Given info:

A candle from a concave mirror, $u=38\text{cm}$

Radius of curvature, $r=24\text{cm}$

Formula used:

Radius of curvature, $r=2f$

Mirror formula, $1/v+1/u=1/f$

Calculation:

Focal length of concave mirror,

$f=-r/2=-24/2=-12\text{cm}$

To determine

(b) To determine:

Where will the image of the candle be located?

Answer to Problem 10P

Solution:

Explanation of Solution

Calculation:

Mirror formula, $1/v+1/u=1/f$

Substituting the given values

$\begin{array}{l}1/v-1/35=-1/12\\ =-1/12+1/35=-38+12/456\\ =-26/456\\ v=-17.53\text{cm}\end{array}$

To determine

(c) To determine:

Will the image be upright or inverted?

Answer to Problem 10P

Solution:

Inverted

Explanation of Solution

As the image of the candle be located at negative 17.53 cm, so image will be inverted