find the value of angle of reflection

Question

Ordinary light incident on a glass slab at the polarizing angle suffers of deviation of 22 degree the value of angle of reflection ?

now what I thought is that when polarization take place the Brewster's law is valid and
$tan\theta_p=\mu $ where $\mu=$ refractive index of slab
and if its a glass slab so it would be 1.5

and since polarizing angle is same as angle of incidence then using brewster law it should come 56 degrees but that comes out to be wrong , then how to do this?

Answer 1

I get the same answer.

There is no need to assume a value for refractive index. At the polarising angle of incidence $\theta_1$, the reflected and refracted rays are at right angles. Therefore
$\theta_1+90^{\circ}+\theta_2=180^{\circ}$
$\theta_1+\theta_2=90^{\circ}$.
We are told that the deviation is
$\theta_1-\theta_2=22^{\circ}$.
Therefore by addition
$2\theta_1=112^{\circ}$
$\theta_1=56^{\circ}$

What answer is in your book?

Comments

answer given is 56 ;  also I understood that we need not assume refractive index as 1.5. :)

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One thing I couldn't understand why deviation$ \theta_1  - \theta_2 $. ?
Can't we take it wrt reflected ray then it would be 180 -2i ?

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Make a sketch, then you will see. $\theta_1$ is angle of incidence, $\theta_2$ is angle of refraction. $\theta_1 - \theta_2$ is angle of deviation.

No, $180-2i=180-112=68$. It should be $22$.

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Since 68 comes that is why we take wrt to refracted ray ? because we needed 22  so it means the given deviation is wrt refracted ray is it ?

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http://www.dictionary.com/browse/angle-of-deviation

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Well, okay understood  :)