Question

The magnification produced when an object is placed at a distance of 20 cm from a spherical mirror is +1/2. Where should the object be placed to reduce the magnification to +1/3.

Answer 1

1. We know that magnification (M) is given by the formula: M = -v/u, where v is the image distance and u is the object distance.
2. We are given that M = +1/2 and u = -20 cm (since the object is placed in front of the mirror). Substituting these values into the formula, we get: +1/2 = -v/-20. Solving for v, we find v = +10 cm.
3. Now, we need to find the new object distance (u') to achieve a magnification of +1/3. Using the same formula, we have: +1/3 = -v/u'. We know that v remains the same (v = +10 cm). Therefore, we can solve for u': +1/3 = -10/u'. Solving for u', we get u' = -30 cm.
4. The object should be moved from its initial position of -20 cm to a new position of -30 cm.