Question 1 A beam of unpolarised light is incident on a detector ...

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Question 1
A beam of unpolarised light is incident on a detector measuring its intensity.
Two linear polarisers and two half-wave plates are provided. The orientations of the fast and slow axes on the wave-plates are not marked. Suggest and explain a method for alignment of the axes of the two wave-plates. Is it possible to distinguish the following two configurations when (a) the fast axes of the wave-plates are aligned and (b) the fast and slow axes of the wave-plates are aligned? Justify your answer using appropriate mathematical derivations describing the modification of light polarisation when it propagates through the system of two linear polarisers and two wave-plates.
Question 2
Consider a Fabry-Perot interferometer. Monochromatic light is incident on the interferometer and the transmitted light intensity is measured. Calculate the reflectivity of the mirrors if the minimum transmitted intensity obtained by tuning the wavelength of the incident light corresponds to 30% of the maximum transmitted intensity.
Question 3
Light with wavelength 500 nm is incident normally on a Fabry-Perot interferometer consisting of two mirrors with an air gap between them. A minimum in the transmitted intensity is observed. The mirrors are moved to a new position with a smaller gap between them, where the light intensity is at its maximum. When the width was changed, the intensity passed through three maxima and three minima before reaching a maximum. By how much was the width of the air gap changed?
Question 4
Light having a mixture of two wavelengths 500.01 nm and 500.02 nm is incident normally on a Fabry-Perot interferometer consisting of two mirrors having reflectivity R=0.9 and separated by an air gap. Find the minimum thickness of the air gap so that the two wavelengths could be resolved using this interferometer?

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