State Brewster's law . Show that the ref...

State Brewster's law . Show that the reflected and refracted rays are normal to each other at the polarising angle of incidence.

Text Solution

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The tangent of the polarising angle is equal to the refractive index of the medium.

From Brewster.s law
`n=tanthetap=(sintheta_(p))/(costheta_(p))=(sintheta_(p))/(cos(90-theta_(p)))`……………..`(1)`
From Snell.s law
`n=(sini)/(cosr)=(sintheta_(p))/(cosr)`.............`(2)`
From `(1)` & `(2)` we get
`sin(90-thetap)=sinr`
`90-thetap=r` or `thetap+r=90^(@)`
But angle `MON=180^(@)`,
Hence reflected and reffracted rays are perpendicular.

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If a ray of light in a denser medium strikes a rarer medium at an angle of incidence i , the angle of reflection and refraction are respectively r and r', if the reflected and refracted rays are at right angles to each other, the critical angle for the given pair of media is

`sin^(-1)(tanr')`

`sin^(-1)(tanr)`

`tan^(-1)(sini)`

`cot^(-1)(tani)`

A ray of light enters from a rarer to a denser medium. The angle of incidence is I . Then the reflected and refracted rays are mutually perpendicular to each other . The critical angle for the pair of media is

`sin^(-1)(coti)`

`cos^(-1)(tani)`

`sin^(-1)(tani)`

`tan^(-1)(sini)`

At the polarising angle, the angle between reflected and refracted rays is

`0^(@)`

`180^(@)`

`90^(@) `

`60^(@)`