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

A
40 cm from the convergent lens, same size as the object
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B
20 cm from the convergent mirror, same size as the object
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C
20 cm from the convergent mirror, twice the size as the object
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D
40 cm from the convergent mirror, twice the size as the object
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Solution

## The correct option is A 40 cm from the convergent lens, same size as the object There will be 3 phenomena (i) Refraction from lens (ii) Reflection from mirror (iii) Refraction from lens 1st refraction from lens: u=−40 cm;f=+20 cm ⇒v=+40 cm (image I1) and m1=−1 Reflection from concave mirror: u=−20 cm;f=−10 cm ⇒v=−20 cm (image I2) and m2=−1 2nd refraction from lens u=−40 cm;f=+20 cm ⇒v=+40 cm (image I3) and m3=−1 Total magnification =m1×m2×m3=−1 ∴ Final image is formed at distance 40 cm from the convergent lens and is of same size as the object.

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