COMEDK · Physics · 25. Ray Optics

A point object is placed on the optic axis of a convex lens of focal length \(f\) at a distance of \(2 f\) to the left of it. The diameter of the lens is \(d\). An eye is placed at a distance of \(3 f\) 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 \(\dfrac{d}{2}\)
C \(\dfrac{d}{3}\)
D \(\dfrac{d}{4}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(\dfrac{d}{4}\)

Step-by-step Solution

Detailed explanation

The object is placed at \(u = -2f\). Using the lens formula \(\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}\), we have \(\dfrac{1}{v} - \dfrac{1}{-2f} = \dfrac{1}{f}\), which gives \(\dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{2f} = \dfrac{1}{2f}\). Thus, \(v = 2f\). The image is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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