A light ray of wavelength 610 nm is incident
at an angle θ on the top surface of a block of
polystyrene surrounded by water.
Find the maximum value of θ for which the
refracted ray will undergo total internal re-
flection at the left vertical face of the block.
(Assume the refractive index of water is 1.333,
and the refractive index of polystyrene is
1.487.)
Answer in units of
◦
I looked for the critical angle and then, since its a right angle just get the angle measure that would equal the incident angle at the top
See the 1st link below under Related Questions.
A similar problem was answered.
that link just tells you that question is missing, but it doesnt help answer it
The first link below does have an answer.
Whether it is a complete answer, I wouldn't know.
You have to scroll down quite a bit for
the answer. I am pasting that answer here.
Maybe it will help you get started.
Physics - drwls, Tuesday, March 23, 2010 at 9:48pm
First you have to look up the index of refraction for water, polystyrene and carbon disulfide. Apparently they have not provided you with those numbers.
You can only get total internal reflection when a light ray tries to enter a medium with a lower index of refraction. That is not what happens in Part 1, so the answer to that one is B.
For the others, get the refractive index, see if Total Internal Reflection is possible, and apply Snell's law if refraction is possible.
To find the maximum value of θ for which the refracted ray will undergo total internal reflection at the left vertical face of the block, you need to calculate the critical angle between polystyrene and water.
The critical angle is given by the equation:
sin(θc) = n2 / n1
Where:
θc is the critical angle
n1 is the refractive index of the medium where the light originates (water)
n2 is the refractive index of the medium where the light is incident (polystyrene)
In this case, n1 = 1.333 (refractive index of water) and n2 = 1.487 (refractive index of polystyrene).
Plugging the values into the equation:
sin(θc) = 1.487 / 1.333
Taking the inverse sine (arcsin) of both sides, we get:
θc = arcsin(1.487 / 1.333)
Using a calculator, the value of θc is approximately 54.9 degrees.
Now, since the refracted ray will undergo total internal reflection at the left vertical face of the block (which forms a right angle with the incident surface), the maximum value for θ would be the same as the incident angle at the top of the block, which is θc.
Therefore, the maximum value of θ is approximately 54.9 degrees.