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Q.

Three lenses in contact have a combined focal length of 12 cm. When the third lens is removed the combined focal length is 60/7 cm. The third lens is

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a

A converging lens of focal length 30 cm.

b

A converging lens of focal length 60 cm.

c

A diverging lens of focal length 30 cm.

d

A diverging lens of focal length 60 cm.

answer is C.

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Detailed Solution

$\begin{aligned} f = 12 \\ \frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}} \end{aligned}$

When third lens is removed

$\frac{1}{f^{'}} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$

$\begin{aligned} f^{'} = \frac{60}{7} \\ \frac{1}{12} = \frac{1}{\frac{60}{7}} + \frac{1}{f_{3}} \\ \Rightarrow f_{3} = - 30 \end{aligned}$

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Three lenses in contact have a combined focal length of 12 cm. When the third lens is removed the combined focal length is 60/7 cm. The third lens is