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Two thin lenses are in contact and the focal length of the combination is $80 cm$ . If the focal

length of one lens is $20 cm$ , then which of the following is the power of the other lens?

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+ 1.66 D

+ 4.00 D

- 1.00 D

- 3.75 D

answer is D.

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Detailed Solution

The power of the other lens will be

- 3.75 D

P

is the power of a combination of two given, the lens which power are

P 1 and P 2

we know,

Power = \frac{1}{focal length}

we know,

P = P 1 + P 2

\frac{1}{f_{eq}}

\frac{1}{f_{1}} + \frac{1}{f_{2}}

\frac{1}{80}

\frac{1}{20} + \frac{1}{f_{2}}

\frac{1}{f_{2}}

\frac{1}{80} - \frac{1}{20}

\Rightarrow \frac{1}{f_{2}}

- \frac{3}{80}

\Rightarrow F

- \frac{80}{3}

\Rightarrow F = - 26.666 cm

\Rightarrow F

= - 0.2666 m

Calculate power by,

P = \frac{1}{f}

\Rightarrow P

\frac{1}{- 0.2666}

\Rightarrow P

= - 3.75 D

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