Question

Question 17 (4 points)

Some car mirrors are curved such that the image is smaller than it would be if plane mirrors were used in order to give a wider field of view. If a car is located 25.0 cm away and looks 0.2 times the size it would normally be, find the local length of this mirror.

Question 17 options:

A)

No option is correct

B)

-6.25 cm

C)

-4.25 cm

D)

-5.25 cm

E)

-3.25 cm

Answer 1

Cars use convex mirrors. Magnification:

$$M=h_i/h_o=d_i/d_o=0.2.$$

Convex mirror equation:

$$\frac{1}{f}=-\frac1{d_i}+\frac1{d_o},\\\space\\ \frac{1}{f}=-\frac1{0.2d_o}+\frac1{d_o}=-\frac4{d_o},\\\space\\ \frac{1}{f}=-\frac4{25},\\\space\\ f=25/(-4)=-6.25\text{ cm}.$$