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

Question

An object that is 1.0 cm tall is placed on the principal 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 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?

Please be specific and clear. Thanks!

Explanation / Answer

y = 1 cm (object height)

f = 15 cm

u = 25 cm (object distance)

we know,

1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/15 - 1/25

v = 37.5 cm (image distance)

image is real and inverted

magnification, m = -V/u = -37.5/25 = -1.5

here m > 1

so, image height > object height

image height = m*object height

= -1.5*1

= -1.5 cm

here, '-' sign indicates the image is inverted.

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