What is the meaning of Refraction?

Waves that do not reflect back from a boundary but travel into the new medium instead are said to refract. In one dimension, the wave just moves straight into the new material, adjusting only its speed. In two dimensions, the angle formed by the refracted ray and the boundary will change from the incident angle, because the wave moves at a different speed in the new medium. Let's take a specific example: light waves of frequency, f, in air at θ₁ (measured between the incident ray and the normal to the boundary) travel into water. Water has a higher index of refraction, n, than air, so the light moves more slowly in the water than in the air. It moves with a shorter wavelength but keeps its original frequency.

The best model I have found for picturing this is to imagine that the wavefronts are lines of musicians in a band marching on grass at speed v₁. As they march, they hit a large mud puddle. The water in the puddle slows down the musicians who are trying to march in the mud (higher index of refraction) to a speed v₂. The effect of this change on the progress of the band is to make the lines of musicians in the mud get closer together (smaller λ₂) since they are traveling more slowly. The angle of the refracted ray (measured from the ray perpendicular to the lines of musicians marching in the mud to the normal to the boundary) tends toward the normal (θ₂<θ₁), since only those who have encountered the mud are slowed down.

The index of refraction of any material is always compared to vacuum, which is given as n = 1. (Air's index is 1.0003 and for most purposes can be rounded to 1.0.)  Water has an index equal to 1.333, and most optical glass has an index of about 1.5 to 1.6. Snell's Law gives a relationship between indices of refraction, the angles of incidence and refraction, and speeds in this problem:

where θ₁ is the angle of incidence, θ₂ is the angle of refraction, v₁ is the speed of the wave in medium with n₁, and v₂ is the speed of the wave in medium with n₂.