The distance between object and its two times magnified real image as produced by a convex lens is 45 cm. The focal length of the lens used is _______ cm.

Solution

Physics sir · 3 steps

Real image means object and image are on opposite sides, so the two distances add up to 45 cm.

1. Use magnification. A real image from a convex lens is inverted, so m = v/u = -2. In size, the image distance is twice the object distance: |v| = 2|u|.
2. Find the distances. The object and the real image are on opposite sides of the lens, so |u| + |v| = 45 cm. With |v| = 2|u|, this gives 3|u| = 45, so |u| = 15 cm and |v| = 30 cm.

   1/f = 1/v - 1/u = 1/30 - 1/-15 = 1/30 + 2/30 = 3/30

3. So. Take u = -15 cm and v = +30 cm in the lens formula. This gives f = 30/3 = 10 cm, so the answer is 10.

The common slip: 30. Putting u = +15 cm instead of -15 cm in the lens formula gives 1/30 - 1/15, a focal length of size 30 instead of 10.

The idea to keep. For a real image, object and image sit on opposite sides of the lens, so the gap between them is |u| + |v|. Use the magnification to split it, then apply the lens formula with signs.

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