Optics Question 94

Question: The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image

[IIT-JEE (Screening) 2003]

Options:

A) 1.25 cm

B) 2.5 cm

C) 1.05 cm

D) 2 cm

Show Answer

Answer:

Correct Answer: B

Solution:

Convex lens will form image $ I _{1} $ at it’s focus which acts like a virtual object for concave lens.

Hence for concave lens $ u=+4cm $ , $ f=20 $ $ cm. $

So by lens formula $ \frac{1}{-20}=\frac{1}{v}-\frac{1}{4}\Rightarrow v=5cm $ i.e. distance of final image $ (I _{2}) $ from concave lens $ v=5cm $ by using $ \frac{v}{u}=\frac{I}{O}\Rightarrow \frac{5}{4}=\frac{I}{2}\Rightarrow (I _{2})=2.5cm $



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