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Refraction

 

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The Laws of Refraction

 

Consider a single light ray travelling through a low density material (eg air) and being refracted at the surface of a transparent material with higher density (eg glass).

 

The normal is a line drawn at right angles to the material's surface at the ray's point of entry.

 

The angle of incidence is the angle the light ray makes with the normal.

 

The angle of refraction is the angle the refracted light ray makes with the normal inside the material.

 

 

refraction at a plane surface

 

 

 

1) The incident ray, the refracted ray and the normal at the point of entry are all in the same plane.

 

 

2) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a particular wavelength (Snell's Law).

 


The ratio constant is called the relative refractive index 'n' .
(older texts - the Greek letter 'μ' mu)

 

The relative refractive index between two media where a light ray travels through one medium (#1) and is refracted through the other medium (#2) is given by:

 

 

refraction - Snell's Law

 

 

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Refractive Index

 

 

The refractive index of a single medium can be defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.

 


Here nm is defined as the absolute refractive index

 

 

definition of the absolute refractive index

 

where,

 

co is the velocity of light in a vacuum
cm is the velocity of light in the medium


Let us consider our two materials(#1 & #2 from above). Their absolute refractive indices are given by:

 

refractive index - equation #3

 

dividing the second equation by the first,

 

refractive index - equation #4

 

that is,

 

refractive index - equation #5

 

refractive index - equation #6

 

Snell's Law equation can now be rewritten as:

 

refractive index - equation #7

 

or

 

refractive index - equation #8

 

 

note: when a light ray travels from a less dense medium to a denser medium, it bends towards the normal(and vice versa).

 

 

refraction through several media

 

 

 

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Common refractive indices

 

 

Material

n (λ = 589.29nm)

Water

1.3330

Diamond

2.419

Amber

1.55

Fused silica

1.458

Sodium chloride

1.50

Liquid Helium

1.025

Water ice

1.31

Acrylic glass

1.490 - 1.492

Polycarbonate

1.584 - 1.586

Crown glass

1.50 - 1.54

Flint glass

1.60 - 1.62

Crown glass

1.485 - 1.755

Flint glass

1.523 - 1.925

Pyrex

1.470

Cryolite

1.338

Rock salt

1.516

Sapphire

1.762–1.778

Cubic zirconia

2.15 - 2.18

Moissanite

2.65 - 2.69

 

 

 

 

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