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Find the length of the optical path two media in contact of length $d_{1}$ and $d_{2}$ of refractive indices $μ_{1}$ and $μ_{2}$ respectively :

Question :

(a) $\displaystyle {{\mu }_{1}}{{d}_{1}}+{{\mu }_{2}}{{d}_{2}}$

(b) $\displaystyle {{\mu }_{1}}{{d}_{2}}+{{\mu }_{2}}{{d}_{1}}$

(d) $\displaystyle \frac{{{d}_{1}}+{{d}_{2}}}{{{\mu }_{1}}{{\mu }_{2}}}$

Solution :

Optical path length is the distance travelled by light in vacuum in the same time as the time taken by the light in a given medium.

$\displaystyle Optical\text{ }path\text{ }length\text{ =}\mu t$

Optical path length for 1^st medium = $\displaystyle {{\mu }_{1}}{{d}_{1}}$

Optical path length for 2^nd medium = $\displaystyle {{\mu }_{2}}{{d}_{2}}$

Total Optical path length = $\displaystyle {{\mu }_{1}}{{d}_{1}}+{{\mu }_{2}}{{d}_{2}}$

Hence option (a) is correct.

Find the length of the optical path two media in contact of length d1 and d2