Question

Problem 23.18

Some rearview mirrors produce images of cars to your rear that are smaller than they would be if the mirror were flat.

Part A)

What is a mirror's radius of curvature if cars 18.0({ m ;m}) away appear 0.37 their normal size? Follow the sign conventions. Express your answer to two significant figures and include the appropriate units.

Answer 1

the formula for magnification is given as ::

m = -d_i/d_o

given in the question :: m = 0.37 and d_o = 18 m

so -d_i = m d_o

d_i = - m d_o = - (0.37) (18)

d_i = -6.66 m

Using the mirror equation ::

1/f = 1/d_i + 1/d_o

1/f = 1/(-6.66) + 1/(18)

f = - 10.57 m

radius of curvature is given as

R = 2f = 2 (-10.57) = -21.14 m