Answer to Question #263634 in Physics for Rethabile

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:

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