An object 'O' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm / s. The position of the image from the mirror after 10 s will be at _________ cm.

Solution

Physics sir · 4 steps

First find where the object is after 10 s, then apply the mirror formula with signs.

1. Focal length. For a concave mirror f = R/2 = 100 cm. Measure distances from the pole, taking the side of the incoming light as negative, so f = -100 cm. At the start the object sits exactly at the focus.
2. New object position. In 10 s the object moves 2 × 10 = 20 cm towards the mirror. It is now 80 cm from the pole, between the focus and the mirror, so u = -80 cm.

   1/v = 1/f - 1/u = -1/100 + 1/80 = (-4 + 5)/400 = 1/400

3. Read the sign. v = +400 cm. The positive sign puts the image behind the mirror, so it is virtual. That is what you expect for an object inside the focal length.
4. So. After 10 s the image is 400 cm from the mirror, behind it.

The idea to keep. When an object moves, find its new position first, then use the mirror formula once. An object inside the focus of a concave mirror always gives a virtual image behind the mirror.

Answer from the NTA final answer key. Solution by PrepWiser.