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Question

A point object O is placed on the principal axis of a convex lens of focal length f=20cm at a distance of 40cm to the left of it. The diameter of the lens is 10cm. An eye is placed 60cm to right of the lens and a distance h below the principal axis. The maximum value of h to see the image is

A
zero
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B
2.5cm
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C
5cm
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D
10cm
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Solution

The correct option is B 2.5cm
Given: A point object O is placed on the principal axis of a convex lens of focal length f=20cm at a distance of 40cm to the left of it. The diameter of the lens is 10cm. An eye is placed 60cm to right of the lens and a distance h below the principal axis.
To find the maximum value of h to see the image
Solution:
As per the given criteria,
object distance, u=40cm
focal length, f=20cm
Applying the lens formula, we get
1f=1v1u1v=1f+1u1v=120+1(40)1v=2140v=40cm
So the image is formed at the curvature.
so we get a ray diagram as shown in above fig.
In the above fig.
ΔCDE and ΔCAB are symmetric.
So ABDB=BCECh5=2040h=52=2.5cm
Hence the maximum value of h to see the image is 2.5cm.

968877_794513_ans_8078db2abcea4c59bd8f0c034ca799f8.jpeg

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