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,

Laws of RefractionLaws of Refraction

Incident ray, normal line and Incident ray, normal line and refracted ray are in the same refracted ray are in the same plane. plane.

Snell’s LawSnell’s Law : for light refracting : for light refracting from any one medium to another, the from any one medium to another, the ratio of the sine of the angle of ratio of the sine of the angle of incidence to the sine of the angle incidence to the sine of the angle of refraction is a constant known of refraction is a constant known as the as the index of refraction, nindex of refraction, n

Stated Mathematically:Stated Mathematically:

n = n = Sin of angle of Sin of angle of incidenceincidence

Sin of angle of Sin of angle of refractionrefraction

n is usually stated as n is usually stated as nn1,21,2 which means the index which means the index

of refraction when of refraction when traveling from substance 1 traveling from substance 1 into substance 2. “ninto substance 2. “n22” is ” is

the substance you go “INTO”the substance you go “INTO”

(note: n(note: n2 2 and INTO will and INTO will help you remember) help you remember)

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

pg. 397.pg. 397.

Why do light rays Why do light rays bend?bend?

The light travels at The light travels at a different velocity a different velocity in each substancein each substance

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

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

nn1, 21, 2 = = nn2 2 = = sine angle incidencesine angle incidence = =

vv11 = = λλ11

nn11 sine angle sine angle

refraction vrefraction v2 2 λλ22

Example:Example:A) What is the speed of light in water? A) What is the speed of light in water? Note: You only need to use that part of Note: You only need to use that part of the formula that applies to this question.the formula that applies to this question.

vvair air = 3.00 x 10= 3.00 x 1088 m/s m/s

vvH2OH2O = ? = ?

  nnairair = 1.00 = 1.00

nnH20H20 = 1.33 = 1.33   

nn1,2 1,2 = = nn2 2 = = vv11 = = 1.331.33 = = 3.00 x 103.00 x 1088 m/s= m/s=2.26 x 2.26 x 101088 m/s m/s

nn1 1 vv22 1.00 v 1.00 vH2OH2O

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

B) If the angle of incidence = 45º B) If the angle of incidence = 45º What is the angle of refraction, What is the angle of refraction, when traveling from air into when traveling from air into water? Note: you only need to use water? Note: you only need to use the part of the formula that the part of the formula that applies to this question.applies to this question.

  nn1,21,2 = = sin of angle of incidencesin of angle of incidence sin of angle of refractionsin of angle of refraction

1.331.33 = = sin 45º sin 45º 1.00 sin of the angle of 1.00 sin of the angle of refractionrefraction

  Sin angle r = Sin angle r = sin45º sin45º = 32.1º = 32.1º

1.331.33

CC) when traveling from water back ) when traveling from water back into air?into air?

nn1,21,2 = = sin of angle of incidencesin of angle of incidence

sin of angle of refractionsin of angle of refraction

1.001.00 = = sin 32.1º sin 32.1º

1.33     sin of the angle of 1.33     sin of the angle of refractionrefraction

Sin angle r = Sin angle r = (1.33)(sin32.1º)(1.33)(sin32.1º) = 45º = 45º

1.001.00

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

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

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

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

The formula for calculating The formula for calculating the critical angle:the critical angle:

Sin critical angle = Sin critical angle = nn22 sin 90º sin 90º

nn11

nn2 2 = = sin of critical anglesin of critical angle

nn11 sin of 90 sin of 90

Example: What is the critical Example: What is the critical angle for light rays passing from angle for light rays passing from diamond into water?diamond into water?

nndiamonddiamond = 2.42 = 2.42

nnwaterwater = 1.33 = 1.33  sin critical angle = sin critical angle = nn22 sin 90º sin 90º = = 1.33 sin 901.33 sin 90

= 0.55= 0.55

nn11 2.422.42

critical angle = 33.3ºcritical angle = 33.3º

Sample Problem:Sample Problem:

Air (n= 1.00)Air (n= 1.00)

Oleic acid (n = 1.43)Oleic acid (n = 1.43)

Water (n = 1.33)Water (n = 1.33)

Carbon Disulfide (n = 1.63)Carbon Disulfide (n = 1.63)

Air (n= 1.00)Air (n= 1.00)

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

pg 400 # 7,8,9pg 400 # 7,8,9

Pg 405 # 10,11Pg 405 # 10,11