33. A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it ?

33. A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it ?

(a) 12 cm

(b) 30 cm

(c) 50 cm

(d) 60 cm

Answer :  (c) 50 cm

\(\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\)

\(\frac{1}{20}=\frac{1}{v}-\frac{1}{-30}\)

\(\frac{1}{v}=\frac{1}{20}-\frac{1}{30}=\frac{10}{20\times30}\)

\(\frac{1}{v}=\frac{1}{60}\)

\(v = 60\)

\(x = 60 - 10 = 50 \ \text{cm}\)