Question

A concave cosmetic mirror has a focal length of 50 cm. A 4.0 cm -long mascara brush is held upright 25 cm from the mirror. Use ray tracing to determine the location of its image. Express your answer using two significant figures. Use ray tracing to determine the height of its image.

Answer 1

ho = height of object (brush)
f = focal length
do = dist of object
di = dist of image
hi = height of image

ho = 4 cm do = 25 cm f = 50 cm

di = ? hi = ?

To determine the image distance, use the mirror equation

1/f = 1/do + 1/di
1/(50 cm) = 1/(25 cm) + 1/di

di = -50 cm

Height of image:

hi/ho = - di/do
hi /(4.0 cm) = - (-50 cm)/(25 cm)

hi = 8 cm