Question:
An object is placed at a distance of \(15\,\text{cm}\) from a convex lens of focal length \(10\,\text{cm}\). On the other side of the lens, at its focus, a convex mirror is placed such that final image formed coincides with the object. The focal length of convex mirror is:
An object is placed at a distance of \(15\,\text{cm}\) from a convex lens of focal length \(10\,\text{cm}\). On the other side of the lens, at its focus, a convex mirror is placed such that final image formed coincides with the object. The focal length of convex mirror is:
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If light retraces its path after reflection from a spherical mirror, the object must lie at the centre of curvature of the mirror.
Updated On: Jun 17, 2026
- \(20\,\text{cm}\)
- \(10\,\text{cm}\)
- \(15\,\text{cm}\)
- \(30\,\text{cm}\)
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The Correct Option is B
Solution and Explanation
Step 1: Image formed by convex lens.
Lens formula:
\[
\frac{1}{f}=\frac{1}{v}-\frac{1}{u}
\]
Given:
\[
f=10\,\text{cm}, \qquad u=-15\,\text{cm}
\]
\[
\frac{1}{10}=\frac{1}{v}+\frac{1}{15}
\]
\[
\frac{1}{v}=\frac{1}{10}-\frac{1}{15}
=\frac{3-2}{30}
=\frac{1}{30}
\]
\[
v=30\,\text{cm}
\]
Step 2: Position of mirror. Mirror is placed at focus of lens: \[ 10\,\text{cm} \] to right of lens. Thus image formed by lens lies: \[ 30-10=20\,\text{cm} \] behind mirror. So for mirror: \[ u=+20\,\text{cm} \] For final image to retrace path, object for mirror must be at centre of curvature. Hence: \[ R=20\,\text{cm} \] \[ f=\frac{R}{2}=10\,\text{cm} \] \[ \boxed{10\,\text{cm}} \]
Step 2: Position of mirror. Mirror is placed at focus of lens: \[ 10\,\text{cm} \] to right of lens. Thus image formed by lens lies: \[ 30-10=20\,\text{cm} \] behind mirror. So for mirror: \[ u=+20\,\text{cm} \] For final image to retrace path, object for mirror must be at centre of curvature. Hence: \[ R=20\,\text{cm} \] \[ f=\frac{R}{2}=10\,\text{cm} \] \[ \boxed{10\,\text{cm}} \]
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