Question

Roger wants to determine the distance of the image of an action figure placed at a distance of 15cm from the mirror. He does not know the focal length of the concave mirror but observes that the rays of the sun after reflection from the mirror converges at a point 5cm in front of the mirror. What is the distance of the image of the action figure from the concave mirror?

• A. 5cm in front of the mirror
• B. 7.5cm in front of the mirror
• C. 5cm behind the mirror
• D. 7.5cm behind the mirror

Answer 1

The correct option is B 7.5cm in front of the mirror

We know that the light rays which are parallel to the principle axis of as spherical mirror, converge at the focus of the mirror. Since the light rays from sun are coming from infinity with respect to the mirror, the focal length of the mirror must be 5cm. Then from mirror formula.
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\frac{1}{-5}=\frac{1}{v}+\frac{1}{-15}\frac{1}{V}=\frac{1}{-5}+\frac{1}{15}\frac{1}{v}=\frac{-3+1}{15}v=\frac{15}{-2}=-7.5cm$
Therefore, option B is correct.