# Internal reflection equation question

• GatoGordo
In summary, the conversation discusses the use of refraction angles in different media, specifically in a glass and coating medium. The speaker mentions the x angle, which is the angle inside the glass medium, and explains that in order to achieve a refraction angle of 90° in the coating medium, one must subtract 90° from the x angle. The reason for this is because the angles are defined relative to the surface normal, and using the tangent could lead to multiple possible angles. Therefore, the normal is used as a standard in Snell's Law to determine the critical angle.
GatoGordo
As you can see we have 3 media here. Only focus on the glass and coating medium. Assume an incident ray comes from the air medium and is refracted inside the glass and then it is refracted again in the coating medium. The x angle is the angle inside the glass medium. In this case, if the incident ray,from the air, enters the glass it will create a refracted ray with an angle. This is the x angle. Now, let's say I want the refraction angle of the coating medium to be 90°. Why do I have to subtract 90° from the x angle to achieve this?
nglasssin(90°−x)=ncoatingsin(90°)

Last edited by a moderator:
Look at your equation, without the $90^\circ$ shift, you'll have a negative answer, i.e. a negative index of refraction.

It's because of the way the angles are defined. Angle of incidence and angle of refraction are the angles relative to the surface normal. That picture defines ##\theta## as relative to the horizontal, which is tangent to the surface. The angle of incidence is ##90^\circ - \theta##.

GatoGordo said:
Summary:: Why do we subtract 90° from the incident angle when we want to find at which angle causes a refraction of 90° in a second medium?

Why do I have to subtract 90°
Your angle θ in the diagram needs to be modified to be the angle between the ray and the Normal to the surface (i.e. 90-θ ). It's the angle from the normal of the surface that is what's in the standard version of Snell's Law, which gives you the Critical Angle.

A thought:
Why do we use the normal and not the angle from the tangent?
There is only one Normal but there are any number of possible tangents for aspherical surfaces - so which tangent could you use? The Normal comes to the rescue.

## What is the Internal Reflection Equation?

The Internal Reflection Equation is a mathematical formula used to calculate the angle of reflection when light passes from a more dense medium to a less dense medium.

## How is the Internal Reflection Equation used in science?

The Internal Reflection Equation is used in various fields of science, such as optics, physics, and chemistry. It helps scientists understand and predict the behavior of light when it passes through different materials.

## What is the relationship between the angle of incidence and the angle of reflection in the Internal Reflection Equation?

The angle of incidence and the angle of reflection are equal in the Internal Reflection Equation. This means that the light will reflect back at the same angle it entered the less dense medium.

## What are some real-life applications of the Internal Reflection Equation?

The Internal Reflection Equation is used in the design of optical devices, such as lenses, mirrors, and prisms. It is also used in the study of optical fibers, which are used in telecommunications and medical imaging.

## What factors can affect the accuracy of the Internal Reflection Equation?

The accuracy of the Internal Reflection Equation can be affected by factors such as surface roughness, impurities in the materials, and the presence of other mediums between the two surfaces. Additionally, the equation assumes that the light is passing through a homogeneous medium, which may not always be the case in real-life scenarios.

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