The following figure represents two biconvex lenses L₁ and L₂ having focal length 10 cm and 15 cm respectively. The distance between L₁ L₂ is :

Solution

Physics sir · 4 steps

Parallel in, parallel out: the focus of L₁ must sit exactly on the focus of L₂.

1. After L1. The ray reaches L₁ parallel to the axis, so it bends through the second focus of L₁. That point is 10 cm to the right of L₁, and the figure shows the ray crossing the axis there.
2. Before L2. The ray leaves L₂ parallel to the axis. A convex lens does that only to a ray that passes through its first focus, which is 15 cm to the left of L₂.
3. Same point. The ray crosses the axis only once between the lenses, so these two foci are the same point. The gap between the lenses is the two focal lengths added together.

   d = f₁ + f₂ = 10 cm + 15 cm = 25 cm

4. So. The distance between L₁ and L₂ is 25 cm, which is option (a).

The idea to keep. If a parallel beam comes out of a two-lens system still parallel, the two lenses share a focal point. For two convex lenses, the separation is f₁ + f₂.

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