In order to visually examine sunspots through a telescope we have to reduce the

Question

In order to visually examine sunspots through a telescope we have to reduce the intensity of the sunlight to avoid harming our retina. To accomplish this intensity reduction astronomers have mounted two linear polarizers on their telescope. The second polarizer has its plane of polarization at an angle of 107o relative to the horizontal. If they want a reduction of the intensity of the sunlight by a factor 0.9780, what angle does the polarization plane of the first polarizer have to form with the horizontal? Give the angle in degrees and assume that ?1 < ?2!

Explanation / Answer

Irrespective of the direction of the orientation, any light passing through the first polarizer, the intensity is reduced to half.

I1 = Io /2

For the second polarizer, we have

I2 = I1 cos^2 theta.

I2 = (Io/2) cos^2 theta

given I2/Io =(1- 0.9780) = 0.022

2(0.022) = cos^2 theta

0.044 = cos^2 theta

theta = 77.9

Already the second the polarizer is at 107 above the horizontal so the first polarizer should be

107- 77.9 = 29.1

The first polarizer should be 29.1 degree from the horizontal.

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