Assertion :If $P_{1}$ and $P_{2}$ be the powers of two thin lenses located coaxially in a medium of refractive index $μ$ at a distance d, then the power P of the combination is $P = P_{1} + P_{2} - \frac{P_{1} P_{2} d}{μ}$ Reason: Because for above given system equivalent focal length is given by $F = \frac{f_{1} f_{2}}{f_{1} + f_{2} - d / μ}$ and $P = \frac{1}{F} .$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$F = \frac{f_{1} f_{2}}{f_{1} + f_{2} - d / μ}$

$⟹ \frac{1}{F} = \frac{f_{1}}{f_{1} f_{2}} + \frac{f_{2}}{f_{1} f_{2}} - \frac{d / μ}{f_{1} f_{2}}$

$⟹ \frac{1}{F} = \frac{1}{f_{2}} + \frac{1}{f_{1}} - \frac{d / μ}{f_{1} f_{2}}$

Now we use $\frac{1}{F} = P, \frac{1}{f_{1}} = P_{1}, \frac{1}{f_{2}} = P_{2}$

$⟹ P = P_{1} + P_{2} - P_{1} P_{2} d / μ$

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Assertion :If P1 and P2 be the powers of two thin lenses located coaxially in a medium of refractive index μ at a distance d, then the power P of the combination is P=P1+P2−P1P2dμ Reason: Because for above given system equivalent focal length is given by F=f1f2f1+f2−d/μ and P=1F.

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionF=f1f2f1+f2−d/μ⟹1F=f1f1f2+f2f1f2−d/μf1f2⟹1F=1f2+1f1−d/μf1f2Now we use 1F=P,1f1=P1,1f2=P2⟹P=P1+P2−P1P2d/μ