A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept alongthe same axis with a distance d between them. If a parallel beam of light falling on A leaves B asa parallel beam, then the distance d in cm will be
Question
A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept alongthe same axis with a distance d between them. If a parallel beam of light falling on A leaves B asa parallel beam, then the distance d in cm will be
Solution
The problem involves two lenses, a convex lens (A) and a concave lens (B), with given focal lengths. The light first passes through the convex lens and then the concave lens. The condition given is that a parallel beam of light falling on lens A leaves lens B as a parallel beam.
Step 1: For lens A (convex lens), the light rays are converging at the focus after passing through the lens. The focal length of lens A is given as 20 cm. So, the image formed by lens A will be at a distance of 20 cm on the other side of the lens.
Step 2: This image acts as the object for lens B (concave lens). For a concave lens, the image is always formed on the same side as the object. The light rays appear to diverge from this image after passing through lens B.
Step 3: Given that the light leaving lens B is a parallel beam, this means that the image formed by lens B is at the focus of lens B. The focal length of lens B is given as -5 cm (negative because it's a concave lens).
Step 4: Therefore, the distance between the image formed by lens A and the image formed by lens B is the sum of their focal lengths, i.e., 20 cm (for lens A) - 5 cm (for lens B) = 15 cm.
So, the distance d between the two lenses should be 15 cm.
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