
The length of the optical path of two media in contact of lengths and of refractive indices and respectively is
Answer
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Hint: In order to solve this question, we are going to first see what an optical path actually is and then find the optical paths for the two mediums and respectively. Then, on adding the two refractive indices, we get the total optical path length of the two media in contact.
The optical path of a medium of refractive index and thickness is given by
Complete step by step solution:
First of all let us see what an optical path means
The optical path can be defined as the product of the geometrical length of the original path followed by light through a given system and the refractive index of the medium through which it propagates.
Where, is the refractive index
is the thickness of the medium.
Thus, in medium 1, the thickness is , so the optical path is
In medium 2, the thickness is , so the optical path is
Now, to find the optical path of the two media, we will have to add the two optical paths as obtained above, thus, the optical path becomes
Therefore, the total length becomes
Hence, option is the correct answer.
Note:
This is the optical path length and not to be confused with the optical path difference at any cost. The expression for the optical path difference is . This gives the difference for the two optical paths while for the total optical path, the two optical lengths are added for the final answer.
The optical path of a medium of refractive index
Complete step by step solution:
First of all let us see what an optical path means
The optical path can be defined as the product of the geometrical length of the original path followed by light through a given system and the refractive index of the medium through which it propagates.

Where,
Thus, in medium 1, the thickness is
In medium 2, the thickness is
Now, to find the optical path of the two media, we will have to add the two optical paths as obtained above, thus, the optical path becomes
Therefore, the total length becomes
Hence, option
Note:
This is the optical path length and not to be confused with the optical path difference at any cost. The expression for the optical path difference is
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