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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?

40 cm from the convergent mirror, twice the size as the object

20 cm from the convergent mirror, same size as the object

40 cm from the convergent mirror, same size as the object

20 cm from the convergent mirror, twice the size as the object

Solution:

Correct option is B. 20 cm from the convergent mirror, same size as the object

There will be 3 phenomenon
(i) Refraction from lens
(ii) Reflection from mirror
(iii) Refraction from lens

After these phenomena. Image will be on object and will have same size.
None of the option depicts so this question is Bonus

1st refraction
u = −40 cm; f = +20 cm ⇒ v = +40 cm (image I and m1 = −1;

for refraction u = −20 cm; f = −10 cm ⇒ v = −20 cm (image I and m2 = −1;

2nd refraction
u = −40 cm; f = +20 cm ⇒ v = +40 cm (image I and m3 = −1;

Total magnification = m1 × m2 × m3 = −1 and final image is formed at distance 40 cm from convergent lens and is of same size as the object.