Spherical Mirrors?

Question

A 10.0 cm high object is situated 28.0 cm in front of a convex mirror that has a radius of curvature of 50.0 cm.

(a) Find the image distance (include the sign).

(b) Find the height of the image.

Answer 1

The focus is half the radius of curv. so the focus is 25.0 cm but behind the mirror because its convex. so it's -25.0 cm.

1/f=1/do+1/di
1/-25=1/28+1/di
di=-13.2 cm

hi/ho=-di/do
hi/10=-(-13.2)/28
hi=4.72 cm

So your answers are:
a) -13.2 cm
b) 4.72 cm

Answer 2

When mirrors are spherical, the focal length is 1/2 the radius of curvature. Convex mirror have negative focal lengths.

Use 1/f = 1/do + 1/di

So, since r = 50 cm, f = -25 cm
do = 28 cm

-1/25 = 1/28 + 1/di
-1/25 - 1/28 = 1/di
-53/700 = 1/di
di = -700/53 = -13.2 cm

The sign is negative indicating the image is virtual and upright.

Magnification = |di /do|
M = |-13.2 cm / 28 cm| = .47
The magnification < 1 so the image is enlarged.

So the image will be .47 x the original 10 cm height

Height of image = 10 cm x .47 = 4.7 cm