Question

A shaving or makeup mirror is designed to magnify your face by a factor of 1.40 when your face is placed 20.0cm in front of it
a) What type of mirror is it?
b) Describe the type of image that it makes of your face.
c) Calculate the required radius of curvature for the mirror.

Answer 1

Answer:

(a) convex mirror

(b) virtual and magnified

(c) 23.3 cm

Explanation:

The having mirror is convex mirror.

distance of object, u = - 20 cm

magnification, m = 1.4

(a) As the image is magnified and virtual , so the mirror is convex in nature.

(b) The image is virtual and magnified.

(c) Let the distance of image is v.

Use the formula of magnification.

$m =-\frac{v}{u}\\1.4=-\frac{v}{-20}\\v =28 cm$

Use the mirror equation, let the focal length is f.

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\\frac{1}{f}=\frac{1}{28}+\frac{1}{20}\\\frac{1}{f}=\frac{28+20}{560}\\f=11.67cm$

Radius of curvature, R = 2 f = 2 x 11.67 = 23.3 cm