1a) Unpolarized light of intensity I 0 is incident on three polarizing filters.

Question

1a) Unpolarized light of intensity I0 is incident on three polarizing filters. The axis of the first is vertical, that of the second is 37° from vertical, and that of the third is horizontal. What light intensity emerges from the third filter?

1b.) If sunlight shines straight onto a peacock feather, the feather appears blue when viewed from 23° on either side of the incident beam of sunlight. The blue color is due to diffraction from the melanin bands in the feather barbules. Blue light with a wavelength of 471 nm is diffracted at 23° by these bands (this is the first-order diffraction) while other wavelengths in the sunlight are diffracted at different angles. What is the spacing of the melanin bands in the feather?

Explanation / Answer

1)

intensity from first filter :

I1 = Io/2

intensity from second filter

I2 = I1 Cos2 37 = (Io/2) Cos2 37

intensity from third filter

I3 = I2 Cos2 53 = ((Io/2) Cos2 37) Cos2 53

I3 = Io (0.5) Cos2 37 Cos2 53

I3 = 0.1155 Io

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