Question

An image produced by the mirror with a magnification m=+4. The focal length of the mirror is 20 cm (note that the sign of f is not given). (a) What is the sign of f? (b) How far in front of the mirror is the object located? (c) What is the image distance? (d) Is the image real or virtual? (e) What kind of mirror is that? Make sure to elaborate on part (a)

Answer 1

Magnification produced by mirror is

m = +4

Magnification is positive, so image formed in upright.

Focal length of mirror is  

f = 20 cm

a)

For the convex mirrors , the image formed will be upright and diminished always.

The magnified image can be formed with concave mirrors only.

Focal length of concave mirror is positive.

Hence sign of focal length of mirror is positive..

b)

m = -- = +4

V= -40

Mirror formula ( real positive sign convention)

և ,

- + u -4u

Зи 1 4u2 - 0 9 u = 15 cm

Object distance from mirror is ( in front of mirror)

15 cm

c)

( negative sign indicates image is virtual)

V = -4u = -60 cm

So a virtual mage is formed behind the mirror,

Image distance behind the  mirror is   

60 cm

d)

Image is virtual.

e)

Mirror is a concave mirror.