CBSE Class 12 · 2006 · All India · Geometrical OpticsShort Answer

A beam of light converges to a point

P

. A lens is placed in the path of the convergent beam

12 cm

from

P

. At what point does the beam converge if the lens is
(i) a convex lens of focal length

20 cm

,
(ii) a concave lens of focal length

16 cm

? Do the required calculations.

Solution

The convergent beam makes

P

a \emph{virtual object},

u = + 12 cm

.
(i) Convex,

f = + 20 cm

\frac{1}{v} - \frac{1}{12} = \frac{1}{20} \Rightarrow \frac{1}{v} = \frac{1}{20} + \frac{1}{12} = \frac{3 + 5}{60} = \frac{8}{60} \Rightarrow v = + 7.5 cm

.
(ii) Concave,

f = - 16 cm

\frac{1}{v} - \frac{1}{12} = \frac{1}{- 16} \Rightarrow \frac{1}{v} = - \frac{1}{16} + \frac{1}{12} = \frac{- 3 + 4}{48} = \frac{1}{48} \Rightarrow v = + 48 cm

(i) 7.5 cm (ii) 48 cm (both behind the lens)

CBSE Class 12 Board · 2006 · All India · Subjective