Subjective Type

A plane monochromatic wave of natural light with intensity $$I_0$$ falls normally on a screen composed of two touching Polaroid half-planes. The principal direction of one Polaroid is parallel and that of the other between them. What kind of diffraction pattern is formed behind the screen? What is the intensity of light behind the screen at the points of the plane perpendicular to the screen and passing through the boundary between the Polaroids?

Solution

Natural light can be considered to be an incoherent mixture of two plane polarized light of intensity $$I_0/2$$ with mutually perpendicular planes of vibration. The screen consisting of the two polaroid half planes acts as an opaque half screen for one or the other of these light waves. The resulting differenction pattern has the alterations in intensity (in the illuminated region) characteristic of a straight edge on both side of the boundary.
At the boundary the intensity due to either components is $$\dfrac{(I_0 /2)}{4}$$ and the total intensity is $$\dfrac{I_0}{4}$$. (Recall that when light of intensity $$I_0$$ is incident on a straight edge, the illuminance in front of the edge is $$I_0/4$$).

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