COMEDK · Physics · 25. Ray Optics

A convex lens forms a real image of an object with magnification \(m_1\). The lens is moved towards the object to obtain another real image of magnification \(\mathrm{m}_2\). The image distance is increased by x . The focal length of the lens is

A \(x\left(m_2-m_1\right)\)
B \(\left(\dfrac{m_2}{m_1}\right) x\)
C \(\dfrac{x}{m_2-m_1}\)
D \(\left(\dfrac{m_1}{m_2}\right) x\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\dfrac{x}{m_2-m_1}\)

Step-by-step Solution

Detailed explanation

For a real image by a convex lens, magnification \(m = \dfrac{v}{|u|}\), giving \(v = f(1+m)\). Initial image distance: \(v_1 = f(1+m_1)\) Final image distance: \(v_2 = f(1+m_2)\) Given \(v_2 - v_1 = x\): \(f(1+m_2) - f(1+m_1) = x\) \(f(m_2 - m_1) = x\)…

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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