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 the three rays that locate the image. Using the mirror equation (Eq. 10.8) and the magnification equation (Eq. 10.9), 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 object H=1 cm

focal length f=15 cm

object distance u=25 cm

image distance V=?

this problem belongs to ray optics of optical instrument

now we find image distance

1//V=1/u+1/f

=1/25 + 1/15

V= 25*15/25+15

=9.375 cm

the image distance V=9.4 cm

now we find magnification m= - v/u

= -9.4/25

=- 0.376

so we

the magnifaction value is negative so image is real

the image is inverted compared to object

the magnetifaction m=-Ho/Hi

- 0.376 = - 1/Hi

image height = 1/0.376

=2.7 cm

so the image is taller than the object

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