Two thin lenses, when in contact, produce a combination of power+10D. When they are 0.25m apart, the power reduces to +6D. The focal lengths of the lenses (in m) are
A
0.124 and 0.5
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B
0.125 and 0.125
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C
0.15 and 0.75
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D
0.125 and 0.75
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Solution
The correct option is A0.124 and 0.5 When lenses are in contact P=1F=1f1+1f2⇒10=1f1+1f2 When They are distance d apart P′=1F′=1f1+1f2−df1f2⇒6=1f1+1f2−0.25f1f2 From Equation (i) and (ii) f1f2=116 From equation (i) and (iii) f1+f2=58 Also (f1−f2)2=(f1+f2)2−4f1f2 Hence (f1−f2)2=(58)2−4×116=964 ⇒f1−f2=38 On solving (iv) and (v)f1=0.5m and f2=0.125m