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
• B. $2.5cm$
• C. $5cm$
• D. $10cm$

Answer 1

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

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}⟹\frac{1}{v}=\frac{1}{f}+\frac{1}{u}⟹\frac{1}{v}=\frac{1}{20}+\frac{1}{(-40)}⟹\frac{1}{v}=\frac{2-1}{40}⟹v=40cm$

So the image is formed at the curvature.

so we get a ray diagram as shown in above fig.

In the above fig.

$\Delta CDE$ and $\Delta CAB$ are symmetric.

So $\frac{AB}{DB}=\frac{BC}{EC}⟹\frac{h}{5}=\frac{20}{40}⟹h=\frac{5}{2}=2.5cm$

Hence the maximum value of $h$ to see the image is 2.5cm.