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Wave Optics

Question
CBSEENPH12039053

(a) How does one demonstrate, using a suitable diagram, that unpolarized light when passed through a Polaroid gets polarized?

(b) A beam of unpolarized light is incident on a glass-air interface. Show, using a suitable ray diagram, that light reflected from the interface is totally polarized, when μ = tan iB, where μ is the refractive index of glass with respect to air and iB is the Brewster's angle. 

Solution

 

Polarization of light is referred to as restricting the vibration of light in a perpendicular direction perpendicular to the direction of propagation of wave.

The vibration of particles of light which is parallel to the axis of crystal passes through the Polaroid on passing an unpolarized light. All other vibrations are absorbed and that is why intensity of emerging light is reduced.

The plane of vibration here is ABCD, in which the vibrations of the polarized light is confined and the plane KLMN is called plane of polarization. KLMN is perpendicular to the plane of vibration.

Reflected light is totally polarized, when unpolarized light is incident on the glass-air interface at the Brewster angle iB. This is known as Brewster’s law.

The reflected component OB and refracted component OC are mutually perpendicular to each other, when light is incident at Brewster’s angle.


angle space B O y space plus space angle Y O C space equals space 90 to the power of o

left parenthesis 90 to the power of 0 space minus space bold italic i subscript bold italic B right parenthesis space plus space left parenthesis 90 to the power of 0 space plus space bold italic r right parenthesis space equals space 90 to the power of bold italic o

Now, using Snell’s law, we have

straight mu straight space equals straight space fraction numerator sin straight space straight i over denominator sin straight space straight r end fraction

i = iB and r = (900 – iB)
Therefore,
straight mu straight space equals straight space fraction numerator sini subscript straight B over denominator sin straight space left parenthesis 90 to the power of straight o straight space minus straight space straight i subscript straight B right parenthesis end fraction straight space equals straight space sini subscript straight B over cosi subscript straight B straight space equals straight space tani subscript straight B