Note carefully that both the angle of incidence (i) and refraction (r) are measured with respect to the surface normal. Note also that the incident ray, normal, and refracted ray all lie in the same geometrical plane.

In practice Snell’s law is often written simply as

Now let’s look at an example that make use of Snell’s law.

Example 2

In a handheld optical instrument used under water, light is incident from water onto the plane surface of flint glass at an angle of incidence of 45°.

(a) What is the angle of reflection of light off the flint glass?
(b) Does the refracted ray bend toward or away from the normal?
(c) What is the angle of refraction in the flint glass?

Solution:

(a) From the law of reflection, the reflected light must head off at an angle of 45° with the normal. (Note: The angle of reflection is not dependent on the refractive indexes of the two media.)
(b) From Table 3-1, the index of refraction is 1.33 for water and 1.63 for flint glass. Thus, light is moving from a lower to a higher index of refraction and will bend toward the normal. We know then that the angle of refraction r should be less than 45°.
(c) From Snell’s law, Equation 3-2, we have:

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