A concave spherical mirror has a radius of curvature of 20.5 cm. Find the locati
ID: 1514479 • Letter: A
Question
A concave spherical mirror has a radius of curvature of 20.5 cm. Find the location of the image for the following object distances. For each case, state whether the image is real or virtual and upright or inverted and find the magnification. (In each case, use the correct sign conventions for all answers. If the image is located at infinity, enter the word infinity for the image distance and for the magnification.)
(a) object distance = 39.0 cm
image distance
cm
magnification
real virtual upright inverted no image is formed
(b) object distance = 19.7 cm
image distance
cm
magnification
real virtual upright inverted no image is formed
c) object distance = 10.25 cm
image distance
cm
magnification
real virtual upright inverted no image is formed
Explanation / Answer
focal length = R/2 = 20.5/2 = 10.25 cm
a)
do = 39.0 cm
using formula
1/f = 1/do + 1/di
1/di = 1/10.25 - 1/39
di = 13.9 cm
magnification = - di/do = - 13.9/39 = - 0.356
image is real and inverted.
B)
do = 19.7 cm
using formula
1/f = 1/do + 1/di
1/di = 1/10.25 - 1/19.7
di = 21.36 cm
magnification = - di/do = - 21.36/19.7 = - 1.08
image is real and inverted.
C)
do = 10.25 cm
using formula
1/f = 1/do + 1/di
1/di = 1/10.25 - 1/10.25 = 0
so image is formed at infinite means no image is formed.
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