A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image formed by the combination is a real image at a distance of

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(1) 60 cm from the convex lens. Convex lens: u = -60, f = 30: 1/v = 1/(30) - 1/(60), v = 60 cm. The concave lens is 20 cm away, so this acts as a virtual object 40 cm beyond it: u = +40, f = -120. 1/v = -1/(120) + 1/(40) = 1/(60), v = 60 cm beyond the concave lens, i.e. 80 cm from the convex lens. The mirror is 70 cm from the convex lens, so the converging beam meets it 10 cm before its focus point: virtual object 10 cm behind the mirror. Plane mirror forms a real image 10 cm in front of it, i.e. 70 - 10 = 60 cm from the convex lens.

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image formed by the combination is a real image at a distance of

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