Question:
A concave lens of focal length \(f\) produces an image \(\frac{1}{x}\) times the size of an object. The distance of the image from the lens is:
A concave lens of focal length \(f\) produces an image \(\frac{1}{x}\) times the size of an object. The distance of the image from the lens is:
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For lenses, use \(m = v/u\) and lens formula \(1/v - 1/u = 1/f\). Express u in terms of v and solve for v.
Updated On: Jun 19, 2026
- \(\frac{x f}{x - 1}\)
- \(\frac{f}{x}\)
- \(\frac{(x-1) f}{x}\)
- \(\frac{(x+1) f}{x}\)
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The Correct Option is C
Solution and Explanation
Step 1: Lens formula.
For a lens, \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\) and magnification \(m = \frac{v}{u}\).
Step 2: Express u in terms of v and x.
Given image is \(\frac{1}{x}\) times object size: \(m = \frac{1}{x} = \frac{v}{u} \Rightarrow u = x v\)
Step 3: Apply lens formula.
\[ \frac{1}{v} - \frac{1}{x v} = \frac{1}{f} \Rightarrow \frac{x-1}{x v} = \frac{1}{f} \Rightarrow v = \frac{(x-1) f}{x} \]
Step 4: Conclusion.
The distance of the image from the lens is \(\frac{(x-1) f}{x}\).
For a lens, \(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\) and magnification \(m = \frac{v}{u}\).
Step 2: Express u in terms of v and x.
Given image is \(\frac{1}{x}\) times object size: \(m = \frac{1}{x} = \frac{v}{u} \Rightarrow u = x v\)
Step 3: Apply lens formula.
\[ \frac{1}{v} - \frac{1}{x v} = \frac{1}{f} \Rightarrow \frac{x-1}{x v} = \frac{1}{f} \Rightarrow v = \frac{(x-1) f}{x} \]
Step 4: Conclusion.
The distance of the image from the lens is \(\frac{(x-1) f}{x}\).
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