Question

A candle is placed at a distance of s=9 cm infront of a concave spherical mirror. The mirror forms an image of the candle somewhere o the optic axis. If the mirror's radius of curvature is R=80 cm, find the location of the image on the optic axis with respect to the mirror's vertex.

Express your answer in cm to 1 decimal place.

Answer 1

The mirror's radius of curvature is R = 80 cm.

So, focal length of the mirror = f = R / 2 = 80 cm / 2 = 40 cm.

Focal length of a concave mirror is in front of the mirror, so it is negative.

So, f = - 40 cm.

Object distance = u = - 9 cm.

Hence, image distance v is given by :

1 / f = 1 / v + 1 / u

or, 1 / v = 1 / f - 1 / u = ( u - f ) / uf

or, v = uf / ( u - f ) = { ( - 9 ) x ( - 40 ) / ( - 9 + 40 ) } cm

or, v = + 11.6 cm.

Hence, the image of the candle is located 11.6 cm behind the mirror's vertex.