Question
Hard
Solving time: 5 mins
Q.29. Proceeding from Fermat's principle derive the refraction formula for paraxial rays on a spherical boundary surface of radius R between media with refractive indices n and n'.
Text solutionVerified
Ans. For O1 to be the image, the optical paths of all rays OAO1 must be equal upto terms o f leading order in h Thus
constant
So, and so
(neglecting products ). Then
Now,
or,
or,
Here,
Hence, Constant
Since this must hold for all h, we have
From our sign convention,
so we get,
constant
So, and so
(neglecting products ). Then
Now,
or,
or,
Here,
Hence, Constant
Since this must hold for all h, we have
From our sign convention,
so we get,
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Question Text | Q.29. Proceeding from Fermat's principle derive the refraction formula for paraxial rays on a spherical boundary surface of radius R between media with refractive indices n and n'. |
Topic | Wave Optics |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 |
Upvotes | 41 |