Optical path of light passing through a lens?
Physics Asked by Asher2211 on May 9, 2021
In my book it is written that the geometrical paths ABE,ACE and ADE are different but the optical paths are equal because each path leads to the same phase difference (i.e. the phase difference between the points A and E)
The optical path length of light in a medium is the distance in which the light would have travelled in the same time if it were travelling in vaccum.
The path ABE is longer than the path ACE and the medium is same, so how then can the optical path be same for both paths?
If the optical paths are different shouldn’t the phase difference between the points A and E be different?
2 Answers
Path ABE it’s not longer than path ACE. It takes light longer to travel through glass than air. So even though path C is straight and looks shorter, the light has more glass to travel through at that point than any of the other paths. The lens is designed to make sure light reaches E at the same time no matter what path it takes. That’s why glasses help us see, by gathering a larger area of light and focusing it where it matters.
Correct answer by Bill Alsept on May 9, 2021
The diagram does not exactly represent the correct paths within the lens. Instead, the portions for B and D should be horizontal lines parallel to the line for C. Then, it will be clear to see that the horizontal paths for B and D are shorter than the path for C. Similarly, the paths outside of the lens are longer for B and D than for C.
Next, we know that the index of refraction is larger inside the lens than outside of the lens. If we compare ABE and ACE, ABE travels more distance outside of the lens (where the index is smaller) and less distance inside the lens (where the index is larger). It is thus plausible that the sum of the optical paths will be the same.
To show that the optical paths are indeed exactly the same, some geometry taking into account the angles of incidence/refraction as the light enters and exits the lens plus some algebra will be necessary.
Answered by Quantum Mechanic on May 9, 2021
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