CBSE Class 12 · 2016 · Delhi · Geometrical OpticsShort Answer

(a) Calculate the distance of an object of height

h

from a concave mirror of radius of curvature

20 cm

, so as to obtain a real image of magnification

2

. Find the location of the image also.
(b) Using the mirror formula, explain why a convex mirror always produces a virtual image.

Solution

(a) Concave mirror:

f = - \frac{R}{2} = - 10 cm

. Real image, magnified

2 \times

and inverted

\Rightarrow m = - 2 = - \frac{v}{u} \Rightarrow v = 2 u

\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{2 u} + \frac{1}{u} = \frac{1}{- 10} \Rightarrow \frac{3}{2 u} = - \frac{1}{10} \Rightarrow u = - 15 cm, v = - 30 cm

(b) Convex mirror:

f > 0

; for a real object

u < 0

. From

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

, both terms are positive, so

v > 0

always — the image is \emph{virtual} (behind the mirror) for every position of a real object.

CBSE Class 12 Board · 2016 · Delhi · Subjective