Laws of Refraction Incident ray, normal line and refracted ray are in the same plane. Snell’s Law : for light refracting from any one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant known as the index of refraction, n

Stated Mathematically: n = Sin of angle of incidence Sin of angle of refraction Sin of angle of refraction

n is usually stated as n 1,2 which means the index of refraction when traveling from substance 1 into substance 2. “n 2 ” is the substance you go “INTO” n is usually stated as n 1,2 which means the index of refraction when traveling from substance 1 into substance 2. “n 2 ” is the substance you go “INTO” (note: n 2 and INTO will help you remember)

The following table gives indices of refraction for various substances (from air into substance) Text has additional information on The following table gives indices of refraction for various substances (from air into substance) Text has additional information on pg pg. 397.

Why do light rays bend? The light travels at a different velocity in each substance The light travels at a different velocity in each substance

“n” represents the number of times faster light travels in air than in the given substance “n” represents the number of times faster light travels in air than in the given substance

Therefore, Snell’s Law is also proportional to the relative velocities of the substances, and therefore their wavelengths. Therefore, Snell’s Law is also proportional to the relative velocities of the substances, and therefore their wavelengths.

n 1, 2 = n 2 = sine angle incidence = v 1 = λ 1 n 1 sine angle refraction v 2 λ 2 n 1 sine angle refraction v 2 λ 2

Example: A) What is the speed of light in water? Note: You only need to use that part of the formula that applies to this question. v air = 3.00 x 10 8 m/s v H2O = ? n air = 1.00 n air = 1.00 n H20 = 1.33 n 1,2 = n 2 = v 1 = 1.33 = 3.00 x 10 8 m/s=2.26 x 10 8 m/s n 1 v v H2O n 1 v v H2O

Note: If the speed is lower in the second medium the rays will bend towards the normal. (the angle of refraction will be smaller than the angle of incidence)

B) If the angle of incidence = 45º What is the angle of refraction, when traveling from air into water? Note: you only need to use the part of the formula that applies to this question. n 1,2 = sin of angle of incidence n 1,2 = sin of angle of incidence sin of angle of refraction sin of angle of refraction 1.33 = sin 45º 1.00 sin of the angle of refraction Sin angle r = sin45º = 32.1º

C ) when traveling from water back into air? n 1,2 = sin of angle of incidence sin of angle of refraction sin of angle of refraction 1.00 = sin 32.1º 1.33 sin of the angle of refraction Sin angle r = (1.33)(sin32.1º) = 45º

Critical Angle For light rays passing from a substance of higher refractive index to one of lower refractive index, there is a certain angle of incidence for which the refracted ray makes a right angle with the normal and comes out along the surface between the two media.

Any angle larger than this critical angle will cause the light ray to show total internal reflection.

Why does this happen when going from higher to lower but not when going from lower to higher?

Because the angle of refraction is greater than the angle of incidence

The formula for calculating the critical angle: Sin critical angle = n 2 sin 90º n 1 n 1 n 2 = sin of critical angle n 1 sin of 90 

Example: What is the critical angle for light rays passing from diamond into water? n diamond = 2.42 n water = 1.33 sin critical angle = n 2 sin 90º = 1.33 sin 90  = 0.55 n critical angle = 33.3º

Sample Problem: Air (n= 1.00) Oleic acid (n = 1.43) Water (n = 1.33) Carbon Disulfide (n = 1.63) Air (n= 1.00)

Given: the angle of incidence from air into oleic acid is 36.9º and light ray continues through column.

pg 400 # 7,8,9 Pg 405 # 10,11