# Find the Angle of Incidence for Total Internal Reflection in a Glass Sphere

• betaleonis
In summary, the conversation discusses the angle of incidence for a ray of light incident on a glass sphere with a refractive index of sqrt 3. Through the use of the equation μ = sin i/sinr and the observation that the triangle formed by the incident ray and the two emerging rays is isosceles, it is determined that the angle of incidence is 60° and the angle of refraction is 30°. The question of why the angle <ABO is equal to the angle of refraction is also addressed and explained as a result of the isosceles triangle formed by the incident ray and the two emerging rays.
betaleonis

## Homework Statement

A ray of light incident on a glass sphere (refractive index sqrt 3) suffers total internal reflection before emerging out exactly parallel to the incident ray. What was the angle of incidence?

μ = refractive index of the glass sphere, i = angle of incidence, r = angle of refraction

μ = sin i/sinr

## The Attempt at a Solution

From the figure, it turns out that < AOE = i (since L1 is parallel to L2, the corresponding angles are equal)

i = 2r, which implies that sin i/ sinr = μ, or 2cosr = μ, or r = 30° and i = 60°, which is the answer.

I do not understand why < ABO = r. Why is it so? It'd be helpful if I someone could come up with a different way of approaching the problem.

#### Attachments

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betaleonis said:
I do not understand why < ABO = r. Why is it so?

I do not understand why < ABO = r. Why is it so? It'd be helpful if I someone could come up with a different way of approaching the problem.
ΔABO is an isosceles triangle: |OA|=|OB|

 beaten to it :)

Oops! I ought to have thought a bit more before posting that question. Thank you. :)

No worries. Everyone does it sometimes :)
You'd probably have noticed right away if the diagram was constructed rather than sketched, even though you noticed about the equal base-angles.

## 1. What is the angle of incidence?

The angle of incidence is the angle at which an incoming ray of light or other electromagnetic radiation strikes a surface or interface between two mediums.

## 2. Why is the angle of incidence important?

The angle of incidence is important because it determines how light or other radiation will interact with a surface. It affects things like reflection, refraction, and diffraction, which are crucial in understanding how light behaves.

## 3. How do you find the angle of incidence?

The angle of incidence can be found using the law of reflection or the Snell's law of refraction. The angle of incidence is equal to the angle between the incident ray and the normal to the surface or interface.

## 4. What factors can affect the angle of incidence?

The angle of incidence can be affected by the angle of the incoming ray, the nature of the surface or interface, and the properties of the medium through which the light is passing. It can also be affected by the wavelength and polarization of the incoming light.

## 5. How does the angle of incidence relate to the angle of reflection?

According to the law of reflection, the angle of incidence is equal to the angle of reflection. This means that the incoming ray of light and the reflected ray will make the same angle with the normal to the surface or interface.

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