# Solving for Index of Refraction: 110 Degrees Angle

• matt72lsu
In summary, the problem involves using the Brewster's angle formula to find the index of refraction of varnish, given that the angle between the incident and reflected rays is 110 degrees. However, the trick is that the problem gives the sum of the incident and reflected angles, rather than the individual angles themselves. By setting the angles to the normal equal and using a diagram, the angle of incidence can be found and used to solve for the index of refraction.

## Homework Statement

While studying physics at the library late one night, you notice the image of the desk lamp reflected from the varnished tabletop. When you turn your Polaroid sunglasses sideways, the reflected image disappears.

If this occurs when the angle between the incident and reflected rays is 110 degrees, what is the index of refraction of the varnish?

## Homework Equations

tan theta = n2/n1

## The Attempt at a Solution

I used n2 = air (1) and solved for n1 but was incorrect. Where am I going wrong?

Well because it is reflected, it sounds like you have a case of total internal reflection. You'll need to use sinC = 1/n.

matt72lsu said:

## Homework Statement

While studying physics at the library late one night, you notice the image of the desk lamp reflected from the varnished tabletop. When you turn your Polaroid sunglasses sideways, the reflected image disappears.

If this occurs when the angle between the incident and reflected rays is 110 degrees, what is the index of refraction of the varnish?

## Homework Equations

tan theta = n2/n1

## The Attempt at a Solution

I used n2 = air (1) and solved for n1 but was incorrect. Where am I going wrong?

Ah so close. You are correct in using the Brewster's angle formula. However notice the trick in the problem. They tell you the angle between the rays NOT the angle the rays make with normal.

so would i do 180-110 or something like that? the angle thing is messing me up

matt72lsu said:
so would i do 180-110 or something like that? the angle thing is messing me up
No.
During reflection angle of incidence is equal to angle of reflection. In the problem, the sum of the angle of incidence and angle of reflection is given. from that find the angle of incidence which is the polarizing angle.

Yes what rl.bhat said is correct. If you are still having trouble thinking about it, try drawing a diagram and setting the reflected and incident angles to the normal equal. Also set the angle between the two rays equal to 110.