A convex mirror has a radius of curvature whose magnitude is 43 cm. The mirror i
ID: 1500023 • Letter: A
Question
A convex mirror has a radius of curvature whose magnitude is 43 cm. The mirror is positioned on a horizontal optical bench with its front surface at 0 cm. A 8.5 cm long fluorescent lamp oriented vertically is placed at +98 cm. What is the focal length of the mirror? At what distance from the mirror can we find a sharp image of the lamp? How tall is the image of the lamp? If the convex mirror were replaced by a plane mirror and the lamp moved to 184 cm from the plane mirror, how tall would the image be?
Explanation / Answer
R = radius of curvature = 43 cm
f = focal length = - R/2 = - 43/2 = - 21.5 cm
ho = height of lamp = 8.5 cm
do = distance from mirror = 98 cm
using the mirror equation
1/f = 1/do + 1/di
1/(-21.5) = 1/98 + 1/di
di = - 17.63 cm distance of image from mirror
using the magnificatiobn equation
hi/ho = - di/do
hi/8.5 = - (-17.63) / 98
hi = 1.53 cm