Refraction Bending of light

Smooth surface Wheels of a car Rough Surface Wheels slow down on rough surface

Smooth surface Wheels of a car Rough Surface øiøi ø i = incident angle ørør ø r = refracted angle Normal (perpendicular to boundary) The rough surface causes a bent path of the wheels.

Wave crests of light Light path Note that the refracted wavelength r is shorter. i r air water The light waves slow down in the water. What about how light travels through a medium?

air water øiøi ø i = incident angle ørør ø r = refracted angle Normal (perpendicular to boundary) The new medium causes a bent path of the light waves. So are these two angles predictable? If so, how?

air water øiøi ø i = incident angle ørør ø r = refracted angle Normal (perpendicular to boundary) The angle of refraction depends on the properties of the two medium through which light travels and also the angle of incidence.

air water øiøi ørør nini nrnr If light slows down in water, then by how much? The answer depends on the material. So each material has associated with it an INDEX of REFRACTION (n medium ) which indicates by what factor light slows down in the medium. n medium = c no medium v medium

air water øiøi ørør nini nrnr n medium = c no medium v medium What then is the index of refraction for a vacuum? Because the speed of light in a vacuum is C, the index of refraction for a vacuum must be Can the index of refraction ever be less than 1? NO - v medium is less than or equal to c, so n is always ≥ 1.00 Index of Refraction

air water øiøi ørør nini nrnr If the material really slows down light, will ø r increase? No, in fact, ø r will decrease. So the more a medium slows down light, the more it bends the pathway. (Imagine wheels.) Willebrod Snell ( ) formalized the relationship between the indices of refraction and the angles with n i sin ø i = n r sin ø r Snell’s Law of Refraction

To summarize, we have: For n r > n i, light is refracted towards the normal in n r. For n r < n i, light is refracted away from the normal in n r. n i sin ø i = n r sin ø r Snell’s Law of Refraction air water øiøi ørør nini nrnr air water ørør øiøi nrnr nini Note that if light is reversed, then the same angles must hold true.

Wave crests of light Light path The speed of light can be compared between media: n 1 v 1 = n 2 v 2 i r air water The light waves slow down in the water.

Wave crests of light Light path Note that the refracted wavelength r is shorter. What about the frequency? What happens to color? i r air water The light waves slow down in the water.

Recall that c = f or for a medium like water v medium = f medium. Note that both the velocity v of the wave and wavelength of the wave are proportional and so if the velocity v decreases then wavelength will decrease too. So what does that suggest about the frequency f ? Frequency f must stay the same!!!! How do we know? Frequency f is related to color, so do colored objects have the same color under water as above water (assuming no absorption of light by water)? What happens to light frequency in a medium like water?

Applications of Refraction Mirages Dusk, dawn, a clear blue sky Rainbows CDs, DVDs A diamond’s “fire”