Question

A point object is placed on the optic axis of a convex lens of focal length \( f \) at a distance of \( 2f \) to the left of it. The diameter of the lens is \( d \). An eye is placed at a distance of \( 3f \) to the right of the lens and a distance \( h \) below the optic axis. The maximum value of \( h \) to see the image is

• A. \( d \)
• B. \( \frac{d}{2} \)
• C. \( \frac{d}{3} \)
• D. \( \frac{d}{4} \)

Hint:

In lens problems, remember the object-image relationship and use the lens formula to determine image distance and height of the image.

Answer 1

The Correct Option is D

For the given setup, the image formed by the convex lens will be real and inverted since the object is placed at a distance of \( 2f \). According to the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where \( u = -2f \) and \( v \) is the image distance. Solving for \( v \), we get: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{2f} \] Thus: \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{2f} = \frac{1}{2f} \] So, \( v = 2f \). The image is formed at a distance of \( 2f \) to the right of the lens. The maximum height \( h \) at which the eye can still see the image corresponds to the maximum angular deviation, which is at \( \frac{d}{4} \) below the optic axis. Thus, the correct answer is (D).