(i) A screen is placed at a distance of $100\ \mathrm{cm}$ from an object. The image of the object is formed on the screen by a convex lens for two different positions of the lens separated by $20\ \mathrm{cm}$. Calculate the focal length of the lens used. (ii) A converging lens is kept coaxially in contact with a diverging lens --- both lenses being of equal focal length. What is the focal length of the combination?

CBSE Class 12 · 2016 · All India · Geometrical OpticsShort Answer

(i) A screen is placed at a distance of

100 cm

from an object. The image of the object is formed on the screen by a convex lens for two different positions of the lens separated by

20 cm

. Calculate the focal length of the lens used.
(ii) A converging lens is kept coaxially in contact with a diverging lens --- both lenses being of equal focal length. What is the focal length of the combination?

Answer: (i) $f = 24 cm$ .
(ii) The combination has infinite focal length (behaves as a plane glass plate).

Solution

(i) By the displacement method, with object--screen distance

D = 100 cm

and separation

d = 20 cm

f = \frac{D ^{2} - d ^{2}}{4 D} = \frac{10 0 ^{2} - 2 0 ^{2}}{4 ( 100 )} = \frac{10000 - 400}{400} = 24 cm

(ii)

\frac{1}{f} = \frac{1}{f} + \frac{1}{- f} = 0 \Rightarrow f_{comb} = \infty

— no net converging/diverging action.

CBSE Class 12 Board · 2016 · All India · Subjective

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CBSE Class 12 · 2016 · All India · Geometrical OpticsShort Answer

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