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Question
The power of a combination of two lenses X and Y is 5 D. If the focal length of lens X be 15 cm :
(a) calculate the focal length of lens Y.
(b) state the nature of lens Y.
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Solution
(a) The focal length of lens X, ie., f1 = 15 cm = 0.15 m
Power of lens X, `p_-1=1/f_1=1/0.15=6.67` D
Let the power and the focal length of the lens Y be P2 and f2, respectively.
The resultant power of the combination of two lenses is the algebraic sum of the powers of the individual lenses.
∴ Power of combination of lenses P = P1 + P2
⇒5 = 6.67 + P2
⇒P2 = 5 - 6.67 = - 1.67 D
The power of the lens is related to the focal length of the lens as:
`p_2=1/f_2`
`-1.67=1/f_2`
`f_2=1/-1.67=0.60`m=-60cm
`f_2=1/-1.67=-0.60m=-60cm`
The focal length of the lens Y is -60 cm.
(b) The focal length of the lens Y is negative. Therefore, the lens is concave and diverging in nature.
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