An object that is 1.0 cm tall is placed on the principle axis of a convex mirror

Question

An object that is 1.0 cm tall is placed on the principle axis of a convex mirror whose focal length is 15.0 cm The base of the object is 25.0 cm from the vertex of the mirror. Make a ray diagram with two or three rays that locate the image. Using the mirror equation and the magnification equation, and the proper sign convention, calculate the image distance and the magnification. Is the image real or virtual? Is the image inverted or upright compared to the object? Is the image taller or shorter than the object?

Explanation / Answer

Height of the object, ho = 1.0 cm
f = - 15.0 cm
Distance of the object, do = 25.0 cm

Using thin lens equation,
1/f = 1/di + 1/do
- 1/15.0 = 1/di + 1/25.0
di = -9.4 cm

Distance of the image, di = - 9.4 cm
(-ve sign mean, Image is behind the mirror.)

M = -di/do
M = 9.4/25.0
M = 0.376

Magnification of the image, M = 0.376

Image is Virtual.
Image is Upright.
Image is shorter than the object.

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