Question

While studying physics at the library late one night, you noticethe image of the desk lamp reflected from the varnished tabletop.When you turn your Polaroid sunglasses sideways, the reflectedimage disappears.
If this occurs when the angle between the incident and reflectedrays is 120^\circ, what is the index ofrefraction of the varnish?

Answer 1

Answer: 1.73

Explanation:

The situation described here is known as polarization by reflection. This was discovered by Scottish physicist David Brewster and then formulated the law that bears his name:

"When a beam of light hits the surface that separates two non-conducting media characterized by different electromagnetic characteristics (electrical permittivity and magnetic permeability), part of it is reflected back to the source medium, and part is transmitted to the second medium."

This polarization happens when the light incides at a specific angle, called the Brewster angle ($\theta_{B}$), which is given by the following formula (taking into account that generally the magnetic permeabilities of the two media involved do not vary):

$tan\theta_{B}=\frac{n_{2}}{n_{1}}$     (1)

Where $n_{2}$ is the index of refraction of the second medium (the varnish in this case) and $n_{1}=1$ is the index of refraction of the first medium (the air).

Now, if we are told the angle between the incident and reflected rays is $120\°$, this means the incident angle is the half ($60\°$), which is the Brewster angle in this case.

So, $\theta_{B}=60\°$   (2)

Rewriting (1) with this incident ray angle:

$tan(60\°)=\frac{n_{2}}{1}$   (3)

$n_{2}=tan(60\°)$  

Finally we obtain the index ofrefraction of the varnish:

$n_{2}=1.732$