COMEDK · Physics · 25. Ray Optics

An object is placed at an unknown distance from a convex objective lens of focal length 8 cm. The objective lens forms a real image which acts as an object for a convex eyepiece of focal length 6.25 cm. The distance between the objective and eyepiece is 45 cm. The microscope is adjusted so that the final image is formed at the least distance of distinct vision (25 cm). Which of the following is correct?

A Object distance = 7.5 cm; Total magnification = 10
B Object distance = 10 cm; Total magnification = 20
C Object distance = 5 cm; Total magnification = 20
D Object distance = 2.5 cm; Total magnification = 10

Verified Solution

Answer & Solution

Correct Answer

(B) Object distance = 10 cm; Total magnification = 20

Step-by-step Solution

Detailed explanation

For the eyepiece, the final image is formed at the least distance of distinct vision, so \(v_e = -25 \text{ cm}\). Using the lens formula for the eyepiece: \(\dfrac{1}{v_e} - \dfrac{1}{u_e} = \dfrac{1}{f_e}\) \(\dfrac{1}{-25} - \dfrac{1}{u_e} = \dfrac{1}{6.25}\)…

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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