Index of refraction when total internal reflection ceases

In summary, the problem involves a light ray incident on a 30°-60°-90° block of zirconium immersed in water. The exit angle of the ray is 46.16° and the substance in the water is changed to increase the index of refraction. The critical angle at which total internal reflection ceases at point P is found using Snell's law and the sum of internal angles in a triangle. The correct value for n2 is not 1.15 as previously thought, but rather when theta critical is less than theta incident, which can be calculated using arcsin(n2/n1).
  • #1
floridianfisher
27
0
light refractions problem

I don't even know where to start with this problem. Can someone please help me out?
As shown in Figure P22.49, a light ray is incident normal to on one face of a 30°-60°-90° block of zircon(n= 1.923) that is immersed in water.


p22-49.gif

Figure P22.49
(a) Determine the exit angle 4 of the ray.
4 = wrong check mark°
(b) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal reflection cease at point P?
n2 =
 
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  • #2
For (a) : The light beam obviously entered at a normal to the shortest side of the triangular block since there wasn't any refraction, so using the fact that a triangle in a plane has a sum of internal angles of one hundred and eighty degrees, [tex]\theta_1=60^\circ [/tex]. And I suppose you know that in one single medium, for a reflection, incident angle equals reflected angle, using this, and Snell's law and the sum of internal angles for a triangle, you should be able to figure this out. Hope this helped.

For (b) : Total internal reflection occurs if critical angle is smaller than incident angle. Using Snell's law, the critical angle is the arcsine of [tex]\frac{n_2}{n_1}[/tex].
 
Last edited:
  • #3
so using the sum of internal angles it looks like theta 3 would be 30 degrees? Because if you split the reflected ray there is a 30-60-90 triangle?
 
  • #4

Homework Statement

As shown in Figure P22.49, a light ray is incident normal to on one face of a 30°-60°-90° block of zircon that is immersed in water.
p22-49.gif

(b) A substance is dissolved in the water to increase the index of refraction. At what value of n2 does total internal reflection cease at point P?


Homework Equations


theta critical= arcsin(n2/n1) and total internal reflection ceases when theta critical is less than theta incident


The Attempt at a Solution


theta 4 is 46.16. I used 59.9=arcsin(n2/1.333) and got n2=1.15 but that's not correct but i don't understand because that is when theta critical is less than theta incident. theta incident is 60
 
  • #5
You need to consider total internal reflection at point P (at [tex]\theta _1[/tex]).

Also n1 is for zirconium.
 

1. What is the definition of index of refraction?

The index of refraction is a measure of how much a material bends or slows down light as it passes through it. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material.

2. What is total internal reflection?

Total internal reflection occurs when a light ray traveling through a material strikes the boundary with another material at an angle greater than the critical angle. This causes the light to be completely reflected back into the original material instead of passing through the boundary.

3. How does the index of refraction affect total internal reflection?

The index of refraction of a material plays a crucial role in determining the critical angle at which total internal reflection occurs. The higher the index of refraction, the smaller the critical angle, meaning that more light will be reflected instead of passing through the boundary.

4. What factors can cause total internal reflection to cease?

Total internal reflection can cease when the angle of incidence of the light ray is decreased below the critical angle. This can occur when the light ray is refracted as it passes through the boundary and exits the material, or when the material's index of refraction is changed by factors such as temperature or pressure.

5. How is the index of refraction measured in a material?

The index of refraction can be measured using various methods, such as Snell's law or the critical angle method. These methods involve measuring the angle of incidence and angle of refraction of a light ray as it passes through the material. The index of refraction can then be calculated using the known values of the incident and refracted angles and the speed of light in a vacuum.

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