2021 Ray Optics and Optical InstrumentsRefraction by Lenses and Reflection by a Plane Mirror Hard Question 26 of 89 in Ray Optics and Optical Instruments

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of:

A 30 cm from the lens, it would be a real image.
B 30 cm from the plane mirror, it would be a virtual image.
C 20 cm from the plane mirror, it would be a virtual image.
D 20 cm from the lens, it would be a real image.

The answer is C.

Solution

Refraction by the lens: u = –60 cm, f = +30 cm ⇒ $v = \frac{uf}{u + f} = \frac{-60 \times 30}{-60 + 30} = 60$ cm
This image is 20 cm behind the mirror and acts as a virtual object;

the mirror forms a real image 20 cm in front of it, i.e. 20 cm from the lens.
Refraction again by the lens (light travelling back): u = –20 cm, f = +30 cm ⇒ $v = \frac{-20 \times 30}{-20 + 30} = -60$ cm So the final image is virtual, 60 cm from the lens,
i.e. 20 cm behind the plane mirror.

Concept image formed by lens-mirror combination

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89 questions from this chapter have appeared across 25 exam years.