Haptic Resistance
Refraction of Light
Refraction is the bending of a wave when it enters a medium where its speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law.

Refraction is responsible for image formation by lenses and the eye.

The bending of refraction can be visualized in terms of Huygens' principle. As the speed of light is reduced in the slower medium, the wavelength is shortened proportionately. The frequency is unchanged; it is a characteristic of the source of the light and unaffected by medium changes.

Refraction and the eyeRefraction of sound

Index of Refraction
The index of refraction is defined as
the speed of light in vacuum divided by the speed of light in the medium.

The indices of refraction of some common substances
are given below with a more complete description
of the indices for optical glasses given elsewhere.
The values given are approximate
and do not account for the small variation of index
with light wavelength which is called dispersion.

Material
n
Material
n
Vacuum
1.000
Ethyl alcohol
1.362
Air
1.000277
Glycerine
1.473
Water
4/3
Ice
1.31
Carbon disulfide
1.63
Polystyrene
1.59
Methylene iodide
1.74
Crown glass
1.50-1.62
Diamond
2.417
Flint glass
1.57-1.75

Snell's Law
Snell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal. Snell's law can be derived from Fermat's Principle or from the Fresnel Equations.

Enter data below, then click the symbol of the quantity you wish to calculate.
Indices of refraction:

Angles with surface normal:

°

°
Enter data and then click on the symbol for the quantity you wish to calculate in the active equation above. The numbers will not be forced to be consistent until you click on the quantity to calculate. Indices of refraction must be greater than or equal to 1, so values less than 1 do not represent a physically possible system.

If the incident medium has the larger index of refraction, then the angle with the normal is increased by refraction. The larger index medium is commonly called the "internal" medium, since air with n=1 is usually the surrounding or "external" medium. You can calculate the condition for total internal reflection by setting the refracted angle = 90° and calculating the incident angle. Since you can't refract the light by more than 90°, all of it will reflect for angles of incidence greater than the angle which gives refraction at 90°.
Fermat's Principle and Refraction
Fermat's Principle: Light follows the path of least time. Snell's Law can be derived from this by setting the derivative of the time =0. We make use of the index of refraction, defined as n=c/v.

This derivation makes use of the calculus of maximum-minimum determination and the definitions of the triangle trig functions.
The Huygens' principle
view permitted a visualization of how light could penetrate into the geometric shadow in a way that the particle view could not.
Law of Reflection
A light ray incident upon a reflective surface will be reflected at an angle equal to the incident angle. Both angles are typically measured with respect to the normal surface. This law of reflection can be derived from Fermat's principle.

The law of reflection gives the familiar reflected image in a plane mirror where the image distance behind the mirror is the same as the object distance in front of the mirror.

Fermat's Principal: Reflection
Law of Reflection

0  =  0
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