Question

The image behind a convex mirror (radius of curvature = 96 cm) is located 2 cm behind the mirror.

(a) Where is the object located?

(b) What is the magnification of the mirror?

(c) Is the image upright or inverted, relative to the object?

(d) Is the image larger or smaller than the object?

Answer 1

(a) 1/f = 1/di + 1/do
f = radius of curvature/2
1/ (48) = 1/(2) + 1/do)
2.08 cm

(b) magnification = -di/do
mag = -(2)/(2.08)
mag = -0.96
(real object located)
relationship between the distances (using the equation of spherical mirror)
(1/o) + (1/i) = (2/R)

convection on the signs: i is negative and R is negative... then
(1/o) - (1/i) = - (2/R)

solve for the distance of real image
o= 1/ ((1/i) - (1/R)) ?2 cm



(magnification of the mirror)
m = - i/o
remember convection on the signs (i is negative)
m = - (- i/o) = i/o = + 0,96

(question c)
m >0 means that the image is not inverted

(question d)
the image is smaller than the real object.