Total Internal Reflection: Finding the angle?

In summary, the figure shows a ray of light entering an optical fiber at an angle of incidence of 51.0°. The index of refraction of the fiber is 2.05. Using Snell's Law, the critical angle is found to be 29.19°. However, when trying to find the angle the ray makes with the normal at the curved surface using the same equation, the answer obtained is 22.27°, which is incorrect according to the online homework system. Further help and clarification is needed to determine the correct angle.
  • #1
longcatislong
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0

Homework Statement



The figure below shows a ray of light entering one end of an optical fiber at an angle of incidence i = 51.0°. The index of refraction of the fiber is 2.05.

Diagram link: http://www.webassign.net/walker/26-55.gif

(a) Find the angle the ray makes with the normal when it reaches the curved surface of the fiber.

Homework Equations



Snell's Law: niSinThetai=ntSinThetat

The Attempt at a Solution



I found theta c (critical angle) to be 29.19 degrees, which correct as verified by my online homework. Then I tried answering part a using niSinThetai=NtSinThetat and got 22.27 degrees as my answer for part a). Online HW system says that's wrong.

Any help is much appreciated! Please tell me what I'm doing wrong and put me on the right track!
 
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  • #2
22.27 degrees is the angle of refraction,θr. Determine θ.

ehild
 

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Related to Total Internal Reflection: Finding the angle?

1. What is total internal reflection?

Total internal reflection is a phenomenon that occurs when a light ray traveling through a medium encounters a boundary with another medium with a lower refractive index. If the angle of incidence is greater than the critical angle, the light ray will be completely reflected back into the original medium instead of refracting into the second medium.

2. How is the angle of total internal reflection calculated?

The angle of total internal reflection can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. The critical angle is then the angle of incidence at which the angle of refraction is 90 degrees.

3. What factors affect the angle of total internal reflection?

The angle of total internal reflection is affected by the refractive indices of the two media, as well as the angle of incidence. A higher refractive index of the first medium or a lower refractive index of the second medium will result in a smaller critical angle. Additionally, the angle of incidence must be greater than the critical angle for total internal reflection to occur.

4. What are some real-life applications of total internal reflection?

Total internal reflection is used in a variety of optical devices, such as fiber optic cables, prisms, and binoculars. It is also responsible for the sparkling effect seen in diamonds, as light entering the diamond is reflected multiple times before exiting.

5. Can total internal reflection occur with any type of light?

Total internal reflection can occur with any type of light, including visible light, infrared light, and ultraviolet light. It is a property of the medium and the angle of incidence, not the specific type of light being used.

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