Reflection and Refraction on a Flat Surface between Two Different Materials

n

1

1.00029

n

2

1.33

n

1

air

n

2

water

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c = 299792458 m/s

v

1

= 299705543 m/s

v

2

= 225407863 m/s

α

i

=

π

4

rad = 45° 0' 0.''

α

r

= 0.56074 rad. = 32° 7' 41.0234''

When a ray of light hits the surface between two different materials, part of it is reflected and part of it is refracted through the second material. Call

α

i

the angle between the incoming ray and the normal to the surface. The angle of reflection is

α

i

, while the angle of refraction is

α

r

, satisfying

n

1

sin(

α

i

)=

n

2

sin(

α

r

)

, where

n

1

and

n

2

are the ratios between the speed of light in a vacuum and in the materials,

n

1

=c/

v

1

and

n

2

=c/

v

2

. There is no reflected ray when

n

1

=

n

2

.

If the angle

α

r

is greater than

90°

, there is total reflection, which means that the ray does not cross the surface. (This is explicitly indicated in the panel on the right as "

α

r

does not exist".)