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Question
A convex lens of power 5 D and a concave lens of power 7.5 D are placed in contact with each other. What is the :
(a) power of this combination of lenses?
(b) focal length of this combination of lenses?
Solution
(a) Power of convex lens P1 = + 5 D
Power of concave lens P2 = - 7.5 D
The combined power is the algebraic sum of the individual powers of the lenses.
∴ Power of the combination P = P1 + P2
P = 5 D - 7.5 D = - 2.5 D
Therefore, the power of the combination of the lenses is - 2.5 D.
(b) The power and focal length are related as:
`p=1/f`
`-2.5=1/f`
∴ f=`-1/2.5=-0.4m=-40 cm`
Therefore, the focal length of the combination of the lenses is 40 cm. The negative sign shows that the combination of the two lenses causes it to behave like a concave lens.
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