CBSE Class 12 · 2020 · Geometrical OpticsLong Answer

(a) With a suitable ray diagram, derive the mirror formula

\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

for a spherical mirror.
(b) A plano-convex lens of radius of curvature

20 cm

is made of glass of refractive index

1.5

. According to the lens maker's formula, find its focal length, and if an object is placed

30 cm

in front of the lens, find the nature and position of the image formed.

Solution

(a) From similar triangles in the mirror ray diagram (

△ A B P \sim △ A^{'} B^{'} P

and

△ A^{'} B^{'} F \sim △ M N P

) with the sign convention (

P B = - u

P B^{'} = v

P F = - f

\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

(b) Plano-convex (

R = 20 cm

, other face flat):

\frac{1}{f} = \frac{μ - 1}{R} = \frac{0.5}{20} \Rightarrow f = + 40 cm

.
Object

u = - 30 cm

\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{40} - \frac{1}{30} = - \frac{1}{120} \Rightarrow v = - 12 cm

(virtual, erect).

f = + 40 cm, v = - 12 cm (virtual image, 12 cm in front of the lens)

CBSE Class 12 Board · 2020 · Subjective