Question:
A screen is placed \(100\,\text{cm}\) from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by \(20\,\text{cm}\). The focal length of the lens is
A screen is placed \(100\,\text{cm}\) from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by \(20\,\text{cm}\). The focal length of the lens is
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In lens displacement method, if object-screen distance is \(D\) and separation between two lens positions is \(d\), then
\[
f=\frac{D^2-d^2}{4D}
\]
Updated On: Jun 26, 2026
- \(18\,\text{cm}\)
- \(24\,\text{cm}\)
- \(25\,\text{cm}\)
- \(30\,\text{cm}\)
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The Correct Option is B
Solution and Explanation
Step 1: Identify the given quantities.
Distance between object and screen is \[ D=100\,\text{cm} \] Distance between the two positions of the convex lens is \[ d=20\,\text{cm} \] This is a lens displacement method problem.
Step 2: Use the lens displacement formula.
For a convex lens forming real images at two positions, \[ f=\frac{D^2-d^2}{4D} \]
Step 3: Substitute the values.
\[ f=\frac{100^2-20^2}{4(100)} \] \[ f=\frac{10000-400}{400} \] \[ f=\frac{9600}{400} \] \[ f=24\,\text{cm} \]
Step 4: Final conclusion.
Hence, the focal length of the lens is \[ \boxed{24\,\text{cm}} \]
Distance between object and screen is \[ D=100\,\text{cm} \] Distance between the two positions of the convex lens is \[ d=20\,\text{cm} \] This is a lens displacement method problem.
Step 2: Use the lens displacement formula.
For a convex lens forming real images at two positions, \[ f=\frac{D^2-d^2}{4D} \]
Step 3: Substitute the values.
\[ f=\frac{100^2-20^2}{4(100)} \] \[ f=\frac{10000-400}{400} \] \[ f=\frac{9600}{400} \] \[ f=24\,\text{cm} \]
Step 4: Final conclusion.
Hence, the focal length of the lens is \[ \boxed{24\,\text{cm}} \]
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