Question

19. 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


(1) A converging lens of focal length 30 cm
(2) A converging lens of focal length 60 cm
(3) A diverging lens of focal length 30 cm
(4) A diverging lens of focal length 60 cm
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Answer 1

$\huge\bold\star\red{QUESTION}\star$

19. 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

(1) A converging lens of focal length 30 cm

(2) A converging lens of focal length 60 cm

(3) A diverging lens of focal length 30 cm

(4) A diverging lens of focal length 60 cm

$\huge\bold\star\red{ANSWER}\star$

Let f1, f2 and f3 be three focal lengths of the lenses.

f=12

f1=f11+f21+f31

When the third lens is removed, f′1=f11+f21

f′=760

121=7601+f31

⇒f3=−30

Since f3 is negative, it is a diverging lens having focal length 30cm.

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