Question

A convex spherical mirror has a radius of curvature of magnitude 32.0 cm. (a) Determine the position of the virtual image and the magnification for object distances of 23.0 cm. Indicate the location of the image with the sign of your answer.

image location	=  cm
magnification

(b) Determine the position of the virtual image and the magnification for object distances of 43.0 cm. Indicate the location of the image with the sign of your answer.

image location

magnification

Answer 1

given

convex mirror of radius of curvature is R = 32 cm

object distance is s = 23 cm

image distance s' = ?

we know the relation is 1/s + 1/s' = 2/R = 1/f

substituting the values  

1/23 +1/s' = 2/32

s' = 52.57 cm

magnification is m = -s'/s = -52.57/23 = -2.286.

-ve sign indicates the image is virtual image  

b) given object distance is s = 43 cm

radius of curvature is R = 32 cm

from relation

1/s + 1/s' = 2/R = 1/f

substituting the values  

1/43 +1/s' = 2/32

s' = 25.48 cm

image location is s' = 25.48 cm

the magnification is m = -s'/s = -25.48/43 = 0.593