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Question
A convex lens of focal length 20 cm is placed coaxially in contact with a concave lens of focal length 25 cm. Determine the power of the combination. Will the system be converging or diverging in nature?
Solution
We have
focal length of convex lens, f1 = +20cm = +0.20 m
focal length of convex lens, f2 = - 25cm = +0.25 m
Equivalent focal length, `F = 1/(f_1)+1/(f_1)=1/20+1/(-25)=1/(100)`
∴ F = 100cm
Power of convex lens, `P_1 = 1/f_1=1/0.20`
Power of concave lens, `P_2 = 1/f_2 = 1/(-0.25)`
Power of the combination, p = p1 + p2
`= 1/0.20 +1/-0.25`
`=100/20 +100/-25`
=`(500 - 400)/100`
=`100/100`
= 1 D
The focal length of the combination = 1 m = 100 cm
As the focal length is in positive, the system will be converging in nature.
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