Path followed by two rays through a thin lens in air are shown- Assume value of - of lens same for both rays -Optical path followed for two rays from A to B is-

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Question

Path followed by two rays through a thin lens in air are shown. (Assume value of $μ$ of lens same for both rays) .Optical path followed for two rays from A to B is:

Greater in case 2 than 1

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Greater in case 1 than 2

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Equal in both the cases

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Value of

μ

is needed to compare

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Solution

The correct option is C Equal in both the cases
Fermat's principle states that the path taken between two points by a ray of light is the path that can be traversed in the least time.
Since a ray takes both the paths, they both must take equal and least time in traversing light. Hence the optical paths must also be the same.
It can be seen from the fact that the lens is thicker at the middle. Hence extra path traveled in air when taken path 2 is equal to the extra equivalent optical path the ray travels through the thick lens when traversing path 1.

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Path followed by two rays through a thin lens in air are shown. (Assume value of μ of lens same for both rays) .Optical path followed for two rays from A to B is:

Path followed by two rays through a thin lens in air are shown. (Assume value of $μ$ of lens same for both rays) .Optical path followed for two rays from A to B is: