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Question: The length of the optical path of two media in contact of length \(\mu _ { 1 }\) and \(\mu _ { 2 }\)...

The length of the optical path of two media in contact of length μ1\mu _ { 1 } and μ2\mu _ { 2 } respectively, is

A

μ1d1+μ2d2\mu _ { 1 } d _ { 1 } + \mu _ { 2 } d _ { 2 }

B

μ1d2+μ2d1\mu _ { 1 } d _ { 2 } + \mu _ { 2 } d _ { 1 }

C

d1d2μ1μ2\frac { d _ { 1 } d _ { 2 } } { \mu _ { 1 } \mu _ { 2 } }

D

d1+d2μ1μ2\frac { d _ { 1 } + d _ { 2 } } { \mu _ { 1 } \mu _ { 2 } }

Answer

μ1d1+μ2d2\mu _ { 1 } d _ { 1 } + \mu _ { 2 } d _ { 2 }

Explanation

Solution

Optical path = μt\mu t

In medium (1), optical path

= μ1d1\mu _ { 1 } d _ { 1 }

In medium (2), optical path

= μ2d2\mu _ { 2 } d _ { 2 }

∴\therefore Total path = μ1d1+μ2d2\mu _ { 1 } d _ { 1 } + \mu _ { 2 } d _ { 2 }