A convex lens of focal length $20\ \mathrm{cm}$ is placed coaxially with a convex mirror of radius of curvature $20\ \mathrm{cm}$. The two are kept $15\ \mathrm{cm}$ apart. A point object is placed $40\ \mathrm{cm}$ in front of the convex lens. Find the position of the image formed by this combination. Draw the ray diagram showing the image formation.

The final image is formed at $\dfrac{50}{3}\ \mathrm{cm}\approx16.7\ \mathrm{cm}$ behind the convex mirror.

CBSE Class 12 · 2014 · Delhi · Geometrical OpticsShort Answer

A convex lens of focal length

20 cm

is placed coaxially with a convex mirror of radius of curvature

20 cm

. The two are kept

15 cm

apart. A point object is placed

40 cm

in front of the convex lens. Find the position of the image formed by this combination. Draw the ray diagram showing the image formation.

Answer: The final image is formed at $\frac{50}{3} cm \approx 16.7 cm$ behind the convex mirror.

\textbf{Lens:}

u = - 40 cm

f = + 20 cm

(object at

2 f

\frac{1}{v} = \frac{1}{20} - \frac{1}{40} = \frac{1}{40} \Rightarrow v = + 40 cm

, i.e. image

40 cm

behind the lens, hence

40 - 15 = 25 cm

behind the mirror — a virtual object for the mirror.
\textbf{Convex mirror:}

f = + 10 cm

u = + 25 cm

\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} + \frac{1}{25} = \frac{1}{10} \Rightarrow \frac{1}{v} = \frac{5 - 2}{50} = \frac{3}{50}

v = \frac{50}{3} cm \approx 16.7 cm behind the mirror

CBSE Class 12 Board · 2014 · Delhi · Subjective