Question

A device called an interferometer is able to measure small changes in distance by measuring the degree of interference between two beams of light. Two coherent beams of light are split off a laser with a frequency of 272500 GHz and travel slightly different paths through space. When you start your experiment the beams from the different paths of the interferometer interfere constructively when combined.   You place piece of a transparent 0.250 micron thick slice of an unknown material so that the second of the two light beams enters perpendicular to the surface and passes through the thickness of the sample. The interference pattern of the combined beams changes when you insert the unknown material. Through experimentation you find that if you lengthen the path of the first beam by 0.300 microns (with the unknown sample present in the second beam) the two beams can return to a state where they constructively interfere (as they were before inserting the sample). What is the index of refraction in the unknown substance?

Please include a sketch of the problem, solve in step-by-step format with explanation, clearly state which equations/principles of physics that are being used, and explain the reasoning behind why your answer is correct. Please and Thank you.

Answer 1

We have calculated the difference in path caused due to insertion on unknown material and we have given that its effect can be nullified by changing path of first source by 0.3 micron so we concluded that the unknow material must have caused a path difference of 0.3 micron, which gave us the value of refractive index of the unknown material.