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Question

Two thin lenses, when in contact, produce a combined power +10 dioptre. When they are 0.25 m apart, the power reduce to +6 dioptre. The power of the lenses in dioptre, are:

A
1 and 9
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B
2 and 8
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C
4 and 6
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D
5 each
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Solution

The correct option is B 2 and 8
Let the two lenses have focal length f1 and f2 meter
In contact, 1F=1f1+1f2= power =10
or, f1+f2f1f2=10.................... (i)
For a separation of d=0.25 m,
1F=1f1+1f2df1f2=6
or, 10df1f2=6
or, f1f2=116 ........................ (ii)
Using (ii) in (i), we get: f1+f2=10×f1f2=1016=58
or, f2=58f1 .................... (iii)
Using (iii) in (ii), we get: f1(58f1)=116
or, f1(1016f1)=1
or, 16f2110f1+1=0
or, f1=12 or 18
f2=18 or 12
So, the power of the lenses are 2 and 8 dioptre.

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