Question:
An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be :
An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be :
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Object at 2f of the lens gives an image at 2f; this image sits at the centre of curvature of the mirror (R = 20 cm), so the rays retrace their path.
Updated On: Nov 5, 2026
- 20 cm from the convergent mirror, same size as the object
- 40 cm from the convergent mirror, same size as the object
- 40 cm from the convergent lens, same size as the object
- 20 cm from the convergent mirror, twice the size of the object
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The Correct Option is C
Solution and Explanation
Lens (f = +20 cm), object at u = -40 cm: \(\dfrac1v = \dfrac1f+\dfrac1u = \dfrac1{20}-\dfrac1{40} = \dfrac1{40}\), so v = +40 cm, magnification \(m_1 = v/u = -1\).
The first image is 40 cm right of the lens, i.e. \(60-40 = 20\) cm in front of the mirror.
Mirror (f = -10 cm), object distance u = -20 cm: \(\dfrac1v = \dfrac1f-\dfrac1u = -\dfrac1{10}+\dfrac1{20} = -\dfrac1{20}\), so v = -20 cm (image at the same point), \(m_2 = -v/u = -1\).
This image is again 40 cm from the lens and acts as a real object for the lens when the light travels back: u = -40 cm, v = +40 cm, \(m_3 = -1\).
Final image: 40 cm from the lens (on the object side, at the object's position), \(|m| = 1\), same size as the object.
Answer: (3) 40 cm from the convergent lens, same size as the object
The first image is 40 cm right of the lens, i.e. \(60-40 = 20\) cm in front of the mirror.
Mirror (f = -10 cm), object distance u = -20 cm: \(\dfrac1v = \dfrac1f-\dfrac1u = -\dfrac1{10}+\dfrac1{20} = -\dfrac1{20}\), so v = -20 cm (image at the same point), \(m_2 = -v/u = -1\).
This image is again 40 cm from the lens and acts as a real object for the lens when the light travels back: u = -40 cm, v = +40 cm, \(m_3 = -1\).
Final image: 40 cm from the lens (on the object side, at the object's position), \(|m| = 1\), same size as the object.
Answer: (3) 40 cm from the convergent lens, same size as the object
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