Question

A concave mirror of radius of curvature 20 cm is shown in the figure. A circular disc of diameter 1 cm is placed on the principle axis of mirror with its plane perpendicular to the principal axis at a distance 15 cm from the pole of the mirror. The radius of disc starts increasing according to the law r = (0.5 + 0.1 t) cm/sec where t is time in second.

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Linked Question 1

In the above question, the area of image of the disc at t = 1 second is :

1.44 π cm²

None of these

1.52 π cm²

1.2 π cm²

At t = 1 sec.

r = 0.5 t + 0.1 t = 0.6 cm

$m = \frac{f}{f - u} = \frac{- 10}{- 10 + 15} = - 2$

⇒ Radius of image = 2r = 1.2 cm

$∴$ Area of image = π(1.2)²

= 1.44 π cm².

Linked Question 2

The image formed by the mirror will be in the shape of a :

Circular disc

Distorted disc

Elliptical disc with major axis vertical

Elliptical disc with major axis horizontal

All dimensions of the disc are perpendicular to the principal axis. Hence all dimensions are equally magnified, resulting in an image in the shape of a circular disc.