In two experiments, light is to be sent along the two paths shown in the figure

Question

In two experiments, light is to be sent along the two paths shown in the figure by reflecting it from the various flat surfaces shown. In the first experiment, rays 1 and 2 are initially in phase and have wavelength ?a. In the second experiment, a slightly longer wavelength, ?b is used, and rays 1 and 2 are once again initially in phase. What least value of distance L is required such that the waves of wavelength ?a emerge from the region exactly in phase but those with wavelength ?b emerge exactly out of phase? State your answer in terms of the two wavelengths?

In two experiments, light is to be sent along the two paths shown in the figure by reflecting it from the various flat surfaces shown. In the first experiment, rays 1 and 2 are initially in phase and have wavelength ?a. In the second experiment, a slightly longer wavelength, ?b is used, and rays 1 and 2 are once again initially in phase. What least value of distance L is required such that the waves of wavelength ?a emerge from the region exactly in phase but those with wavelength ?b emerge exactly out of phase? State your answer in terms of the two wavelengths?

Explanation / Answer

The ray one travels an extra distance of 4L than raytwo. For constructive interference the condition is 4 L = m? m -positive integer For destructive interference, we have 4 L = (k/2)?' k - positive odd integer. from the above two equations (k/2)?' = m? k = 2m ( ? / ?' ) if m = 2 then k = 5. which satisfy theconditions. so substituting m =2 in the first equation 4L =m? 4L = 2? L = ?/2

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