Physics
Physics
Problem
A convex lens of focal length 1 meter and a concave lens of focal length 0.25 meter are kept 0.75 meter apart. A parallel beam of light first passes through the convex lens, then through the concave lens and comes to a focus 0.5 m away from the concave lens.Intuitive explanation
The key is treating this as a two-lens system where the output of the first lens becomes the input to the second. After the convex lens converges the parallel rays toward its focal point, those converging rays hit the concave lens before they meet—this is the crucial setup. The concave lens then redirects them to a new focus point. Use the lens equation twice: first to find where the convex lens would focus alone, then treat that as the object distance for the concave lens, accounting for the separation between them.
Intuitive explanation
The key is treating this as a two-lens system where the output of the first lens becomes the input to the second. After the convex lens converges the parallel rays toward its focal point, those converging rays hit the concave lens before they meet—this is the crucial setup. The concave lens then redirects them to a new focus point. Use the lens equation twice: first to find where the convex lens would focus alone, then treat that as the object distance for the concave lens, accounting for the separation between them.