Question

A man is standing 3.40 m in front of a convex spherical mirror of radius of curvature 4.20 m. How far is the image from the object?

Answer 1

Focal length of the convex mirror f=R/2 =4.20/2 =2.10 m

Using mirror equation

1/f =1/v+1/u 1/v=1/f -1/u ...1

Here f=2.10 m , u= -3.40 m ( I am using cartesian sign convention )

put these value in equation 1

1/v=1/2.10 +1/3.40

1/v= (3.40+2.1)/(2.10*3.40)

=5.50/7.14

v=7.14/5.50=1.298

v=1.30 m (distance of the image from the mirror )

the distance of the image from the object

d=v+3.40=1.30+3.40

d=4.70 m Answer