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Question
A concave mirror produces a real image 1 cm tall of an object 2.5 mm tall placed 5 cm from the mirror. Find the position of the image and the focal length of the mirror.
Solution
Distance of the object from the mirror (u) = -5 cm
Height of the image (hi) = -1 cm
Height of the object (ho) = 2.5 mm = 0.25 cm
We have to find the image distance (v) and the focal length of the mirror (f).
Using the magnification formula, we get
`m=h_i/h_o=(-v)/u`
`or (-1)/0.25=(-v)/-5`
`or v=-5/0.25=-20 `cm
Thus, the distance of the image is -20 cm.
It means that the image will form 20 cm in front of the mirror.
Now, using the mirror formula, we get
`1/f=1/v+1/u`
`1/f=1/-20+1/5`
`or1/f=1/20+1/-5`
`or 1/f=-1/20-4/20=-5/20=-1/4`
f=-4 m
Thus, the focal length of the mirror is 4 cm.
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