Snell's Law and Refraction
A laser beam enters a block of transparent material. Change the angle and the refractive indices and see how the ray bends, how much light is reflected, and when it is totally reflected inside.
Or drag the laser around the point where the beam enters the block.
Make the block wider and the beam steeper to send the ray to the top or bottom face.
Show the physics and the notes
Refraction. Light travels at different speeds in different materials. The refractive index of a material is n = c/v, where c is the speed of light in a vacuum and v its speed in the material. When a ray crosses the boundary between two materials at an angle, the change in speed makes it change direction. Snell’s law gives the angles, measured from the normal (the line at right angles to the surface):
n1 sinθ1 = n2 sinθ2
Going into a material with a higher index (slower light), the ray bends towards the normal. Going into a material with a lower index, it bends away.
Total internal reflection. When light goes from a material of higher index to one of lower index, there is an angle of incidence, the critical angle, at which the refracted ray would travel along the surface (θ2 = 90°):
sinθc = nlower / nhigher
At bigger angles there is no refracted ray at all: all of the light is reflected, which is called total internal reflection. For glass to air θc is about 42° and for diamond to air only 24°, which is why diamonds sparkle. Optical fibres use it too. In this block, a ray that enters through the side face and travels towards the top or bottom face always strikes it at an angle greater than the critical angle (for glass in air), so it is totally reflected.
Parallel faces. The ray enters at the first face with θ1 and leaves the opposite face at the same angle: since the two faces are parallel, the angle of refraction at the first face is the angle of incidence at the second, so n2 sinθ2 = n1 sinθ3 gives θ3 = θ1. The beam is moved sideways but not turned.
Partial reflection. At every surface some light is reflected as well as refracted. The brightness of the rays is worked out with the Fresnel equations (for unpolarised light). At normal incidence the fraction reflected is ((n2 − n1)/(n2 + n1))²: 4% for air to glass, 2% for air to water and 17% for air to diamond. It grows quickly at large angles of incidence. The reflected fraction plus the refracted fraction is always 100%.
The picture is a two-dimensional drawing of the rays only. The colours of the materials are decoration. In a real block the colours spread out a little (dispersion), which is not shown.
Learn more in the Refraction lesson. Rebuilt in the Physics High style.