Importance of Optical Path Length - Graphically - 1D Consider the two sources, e

Question

Importance of Optical Path Length - Graphically - 1D

Consider the two sources, each of which can emit one of two possible wavelengths, shown in the picture below.

If the wavelength is 1

Part A

What is the optical path length from source 1 to P?

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Part B

What is the optical path length from source 2 to P?

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Part C

What is the difference in optical path length ?

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The correct answer does not depend on: 2.

Even though neither wave travels an interger number of wavelengths to get to P, they will both arrive either peak-to-peak or trough-to-trough and therefore will constructively interfere!

If the wavelength is 2

Part E

What is the optical path length from source 1 to P?

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Part F

What is the optical path length from source 2 to P?

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What is the difference in optical path length ?

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Explanation / Answer

The length of the square box interms of 1 is (1)/2 .

The length of the square box in terms of 2 is (2)/4.

Part A : If the wavelength is 1 the optical path length from source 1 to P is (3/2 )1.

part B : In terms of source 1 the optical parth length from source 2 to P is (1/2)1

part C : Opical path length difference is (3/2 - 1/2 )1 = 1

part E : If the source is  2, the optical path length from source 1 to P is  (3/4)2 = (3/2)1

part F : the optical path length from source 2 to P is  (1/4)2 = (1/2)1

part G : the difference in optical path length is (3/4-1/4)2 = (1/2)2 = 1

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