Light reflected in rod (Snell's Law)

In summary, the problem involves a solid glass rod of length 75cm and diameter 1.5cm with an index of refraction of 1.46. The question asks for the maximum angle of incidence for which light entering the center of the end of the rod from air will be totally reflected inside the rod. This can be found by comparing the angle of incidence with the critical angle of the glass rod, which is given by the equation sinC = 1/μ. However, due to the large size of the rod compared to its diameter, this condition cannot be achieved.
  • #1
Jstew
18
0

Homework Statement


Consider a solid glass rod of length 75cm and diameter 1.5cm with n=1.46.
Light enters the center of the end of the rod from the air. What is the maximum angle of incidence for which the light is totally reflected inside the rod?


Homework Equations


n1 sin (A1) = n2 sin (A2)


The Attempt at a Solution


I don't know where to start because I don't know what is meant by "totally reflected inside the rod". Any help would be greatly appreciated!
 
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  • #2
first u can try by drawing how the light enters the rod :)
 
  • #3
http://img692.imageshack.us/img692/8996/glassrod.th.jpg
I've drawn how the light enters the rod, and I understand how to find theta 2 and theta 3 given theta 1 and the indices of refraction, I just don't know what the problem is asking for.
 
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  • #4
as u see from ur picture, if the rod is very long, what will happen to that ray in the picture?
 
  • #5
It will reflect or refract, depending on the angle. But what does it mean to "reflect completely"?
 
  • #6
that means that if the angle that enters the rod is bigger than that, the ray will be refracted that's all
 
  • #7
"totally reflected inside the rod". means the light is not cumming out of the second face. For that θ2 should be equal to or greater than the critical angle of the glass rod which is found by the equation
sinC = 1/μ.
Since the rod is so large compared to its diameter, this condition cannot be achieved. May be one of the dimension is not correct.
 

FAQ: Light reflected in rod (Snell's Law)

What is Snell's Law and how is it related to light reflection in a rod?

Snell's Law is a fundamental principle in optics that relates the angle of incidence and angle of refraction of a light ray as it passes through an interface between two different media. This law is directly applicable to light reflection in a rod, as the angle of reflection can be determined using the angle of incidence and the refractive index of the rod material.

What is the refractive index and how does it affect light reflection in a rod?

The refractive index is a measure of how much a material can bend 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. The higher the refractive index, the more the light will be bent at the interface between the material and the surrounding medium, resulting in a larger angle of reflection in the rod.

How does the angle of incidence affect light reflection in a rod?

The angle of incidence is the angle at which a light ray hits the interface between two media. According to Snell's Law, the angle of reflection is equal to the angle of incidence, so a larger angle of incidence will result in a larger angle of reflection in the rod. This means that as the angle of incidence increases, the reflected light will be more dispersed and less focused.

Can Snell's Law be used to predict the exact angle of reflection in a rod?

No, Snell's Law is a simplified model that assumes the light rays are traveling in a straight line and does not take into account other factors such as the thickness of the rod or any imperfections in the surface. It can provide a close approximation of the angle of reflection, but it cannot predict it with 100% accuracy.

How does the material of the rod affect light reflection?

The material of the rod plays a significant role in light reflection, as it determines the refractive index and therefore the angle of reflection. Different materials have different refractive indices, so the angle of reflection will vary depending on the material of the rod. Additionally, the surface properties of the material can also affect the amount of light reflected, as a smooth surface will reflect more light than a rough surface.

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