The same size images are formed by a convex lens when the object is placed at 20 cm or at 10 cm from the lens. The focal length of convex lens is __________ cm.

Solution

Physics sir · 4 steps

Same size does not mean same image: one is real and inverted, the other virtual and erect, so m = -m'.

1. Two kinds of image. A convex lens gives a real, inverted image when the object is beyond f, and a virtual, erect image when it is inside f. Equal size at two different distances is only possible if 20 cm is beyond f and 10 cm is inside it. So the two magnifications are equal in size but opposite in sign.
2. Magnification formula. From 1/v - 1/u = 1/f and m = v/u, the magnification is m = f/(f + u), with u negative on the object side.

   f/(f - 20) = -f/(f - 10)

3. Solve for f. Cancel f to get f - 10 = -(f - 20) = 20 - f, so 2f = 30 and f = 15 cm. Check: at 20 cm, m = 15/-5 = -3, and at 10 cm, m = 15/5 = +3. Both images are 3 times the object size.
4. So. The focal length of the convex lens is 15 cm.

The idea to keep. When a convex lens makes equal-sized images for two object distances, one image is real and one is virtual. Set m₁ = -m₂; then f is the average of the two distances.

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