A convex spherical mirror has a radius of curvature of magnitude 48.0 cm. Determ
ID: 1610972 • Letter: A
Question
A convex spherical mirror has a radius of curvature of magnitude 48.0 cm. Determine the position of the virtual image and the magnification for object distances of 43.0 cm. Indicate the location of the image with the sign of your answer. image location = _______ cm magnification = _______ Determine the position of the virtual image and the magnification for object distances of 55.0 cm. Indicate the location of the image with the sign of your answer. image location = _______ cm magnification = _______ Are the images in parts (a) and (b) upright or inverted? The image in part (a) is _______ The image in part (b) is _______Explanation / Answer
R = radius of convex mirror = 48 cm
f = focal lenegth of mirror = - R/2 = - 48/2 = - 24 cm
a)
do = object distance = 43 cm
di = image distance = ?
m = magnification = ?
using the mirror equation
1/f = 1/do + 1/di
1/(-24) = 1/43 + 1/di
di = - 15.4 cm
image is located at distance 15.4 cm behind the mirror
magnification is given as
m = - di/do = - (-15.4)/43
m = 0.36
b)
do = object distance = 55 cm
di = image distance = ?
m = magnification = ?
using the mirror equation
1/f = 1/do + 1/di
1/(-24) = 1/55 + 1/di
di = - 16.7 cm
image is located at distance 16.7 cm behind the mirror
magnification is given as
m = - di/do = - (-16.7)/55
m = 0.304
c)
since the magnification in each case is positive , hence the images are upright in both cases