Question

A small candle is 33 cm from a concave mirror having a radius of curvature of 24 cm. A) What is the focal length of the mirror? Follow the sign conventions.
B) Where will the image of the candle be located? Follow the sign conventions.
C) is the image inverted or upright?

Answer 1

Explanation:

It is given that,

Object distance from a concave mirror, u = -33 cm

Radius of curvature of the mirror, R = -24 cm (in front of mirror)

(a) The relation between focal length (f) of the mirror and the radius of curvature is given by :

R = 2 × f

$f=\dfrac{R}{2}$

f = -12 cm

(b) Mirror's formula is given by :

$\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}$, v is the image distance

$\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}$

$\dfrac{1}{v}=\dfrac{1}{-12}-\dfrac{1}{-33}$

v = −18.85 cm

(c) The image formed by a concave mirror is real and inverted. Magnification of the mirror is given by :

$m=\dfrac{-v}{u}$

$m=\dfrac{-(-18.85)}{-33}$

m = -0.57

As the magnification of the mirror is less than 1, so the image is inverted. Hence, this is the required solution.