Question:
For a convex lens, magnifications m_1 and m_2 correspond to object distances u_1 and u_2. The focal length is:
For a convex lens, magnifications m_1 and m_2 correspond to object distances u_1 and u_2. The focal length is:
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Convert magnification into linear equation in u to avoid sign confusion.
Updated On: Jun 10, 2026
- \(\frac{u_2 - u_1}{m_1 - m_2}\)
- \(\frac{m_1 m_2 (u_1 - u_2)}{m_2 - m_1}\)
- \(\frac{u_1 - u_2}{m_2 - m_1}\)
- \(\frac{u_2 - u_1}{m_2 - m_1}\)
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The Correct Option is C
Solution and Explanation
Concept:
For lens:
\[
m = \frac{v}{u}, \quad \frac{1}{f} = \frac{1}{v} - \frac{1}{u}
\]
Eliminating v gives:
\[
m = \frac{f}{f+u}
\]
Step 1: For two cases \[ m_1 = \frac{f}{f+u_1}, \quad m_2 = \frac{f}{f+u_2} \]
Step 2: Solving gives \[ f = \frac{u_1 - u_2}{m_2 - m_1} \] Thus correct option is (C).
Step 1: For two cases \[ m_1 = \frac{f}{f+u_1}, \quad m_2 = \frac{f}{f+u_2} \]
Step 2: Solving gives \[ f = \frac{u_1 - u_2}{m_2 - m_1} \] Thus correct option is (C).
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