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Question
An object is 2 m from a lens which forms an erect image one-fourth (exactly) the size of the object. Determine the focal length of the lens. What type of lens is this?
Solution
Given:
Object distance (u) =-2 m
Image distance (v) = ?
Magnification (m) = 0.25 (one-fourth of the size of the image)
Focal length (f) = ?
Magnification (m) =`v/u`
`0.25=v/-2`
v=-0.5m
Putting these values in lens formula, we get:
`1/v-1/u=1/f`
`1/-0.5+1/-2=1/f`
`1/-0.5+1/2=1/f`
`1/f=1/2-1/0.5`
`1/f=1/2-10/5`
`1/f=(-3)/2`
`f=-0.66` m
Negative sign of focal length shows that lens is diverging in nature. Hence, it is a concave lens.
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