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 Spanish - Chinese The Optics Book - Reflection & Refraction Written by:Tim
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Related Articles:

Total Internal Reflection Applet
Reflection & refraction Applet
Refraction of light Applet
Refracting Astronomical Telescopy Applet
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In this section:

The Optics Book

1. Before Optics
2. Ligth and Ilumination
3. Reflection and refraction

Reflection (2nd Part)
Reflection (3rd Part)
Refraction
Refraction (2nd Part)

4. Geometrical Optics and thin lenses
5. The human eye
6. Optics instruments
7. Scattering & spectrum
8. Color
9. Interferences & difraction
10. Polarization
11. Quantic Optics

## Refraction (Continuation)

The law of refraction is n1sinq1= n2sinq2

To prove it, consider Fig 17 which shows two fixed points A and B in two different media and a refracting ray APB connecting them. The time t for the ray to travel from A to B is given by

t=(L1/ V1)+(L2/ V2)

Using the relation n=c/v we can write this as

t=[(n1L1+ n2L2]/c=L/c

where L is the optical path length defined as

L=n1L1+ n2L2

For any light ray travelling through successive media, the optical path length is the sum of the products of the geometrical path length and the index of refraction of that medium. The equation ln=l/n shows that the optical wave length is equal to the length that this same number of waves would have if the medium were a vacuum. Do not confuse the optical path length with the geometrical path length which is L1+ L2 for the ray of Fig 17.

Fermat's principle requires that the time t for the light to travel the path APB must be a minimum( or a maximum or must remain unchanged) which in turn requires that x be chosen so that dt/dx=0. The optical path length in Fig 17 is

L=n1L1+ n2L2=n1(square root of a2+ x2)+n2(square root of b2+(d-x)2)

Substituting this result into t=[(n1L1+ n2L2]/c=L/c and differentiating, we obtain

Dt/dx=1/c(dL/dx)

=n1/2c(a2+ x2)-1/2(2x)+ n2/2c[b2+ (d-x)2]-1/2 (2)(d-x)(x-1)=0

Which we can write as

n1 [x/( square root of a2+ x2)]=n[(d-x)/ (square root of b2+(d-x)2)]

 FIGURE 17 Credits: Halliday David

Comparision with Fig 17 shows that we can write as n1sinq1= n2sinq2 which is the law of refraction.