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Refraction

 

Refraction is the change in direction of a wave due to a change in its medium (light travelling from medium 1 to medium 2)

The cause is of the change in direction is the difference in speed of light in both media.

 

There is:   

n = sin i/sin r  (Snellius’law of refraction )

 

 i  angle of incidence  (angle between incident ray and normal ) 

r  angle of refraction (angle between refracted ray and normal)

n  index of refraction  

 

Index of refraction of a material 

 

n = (speed of light in vacuum (mostly taken as air)) / (speed of light in the material)

 

 Example 1  

Find the speed of light in glass.

nglass = 1.5

nglass =  cvac / cglass

 

1.5 = (3.00 x 108 )/ cglass

 

cglass = 2.25 x 108 m s-1

 

 

Refraction of light from an optically less dense medium to an optically more dense medium

-          refraction to the normal

-          i > r

Example 2                                                      

Refraction_of_light_from_an_optically_less_dense_medium_to_an_optically_more_dense_medium

    

A ray of light travels from air to glass                                      

The index of refraction of glass is 1.5

 

 

Angle of incidence i is 40 o.

Find the angle of refraction r

         

1.5 = sin 40o/sin r      1.5 sin r = sin 40o    

1.5 sin r = 0.94279       sin r =0.94279/1.5 = 0.428525

 

r = 25o

(Except the refracted ray, there is a reflected ray. This is not shown in the figure)

 

 

Refraction of light from an optically more dense medium to an optically less dense medium

Example : glass → air

 

-          refraction from the normal

-          i < r

 

(The reflected ray is not shown in the figure)                                                                                                                                                                                          

The largest angle of incidence where refraction occurs is called ‘critical angle’ (ic )

Then the angle of refraction is 90o

 

 

           (The reflected ray is not shown in the figure)                                                                                                  

                                                                                        

 

 

 

 

 

 

 

When  i > ic  the ray is totally reflected in the first medium.

This is called : total internal reflection

 

 

 

 Example 3

Calculate the critical angle for the transition from glass to air

 

n glas = 1.5  

This means : n air→glass = 1.5

 

n glass→air  =  1/n air→glass = 1/1.5 = 0.667

 

Law of Snellius:

sin ic/sin 90 = 0.667       sin i c = 0.667     ic = 42o