Physics 20
Light Unit: Refraction and Total Internal Reflection
Refraction of Light
 Refraction is the bending of light
o As we know, light travels in straight lines. But it only travels in straight lines when it travels in a medium of the
same density.
o When light bends because it travels from one transparent medium into another of different density this is
refraction.
 Refraction is responsible for many illusions.
o Fish viewed in water appear nearer to the surface then they actually are.
o Stick or spoon in water appears bent at the surface of the water.
Refraction and the Speed of Light
 In 1850, Foucault (a physicist) demonstrated that light travels slower in water than in air.
o This change in speed causes refraction to occur.
 When light strikes a boundary between two media, the following happens:
o Some of the light is partially reflected. This light is the reflected ray that reflects like a mirrored surface. (This
means the angle of incidence = the angle of reflection.)
o Some of the light enters the water. This light DOES NOT continue along its straight path. Instead this light is
bent as it passes from the air into the water. The path of this ray is the refracted ray.
 NOTE: If the incident ray strikes the second medium at an angle of 90 degrees (perpendicular), then the light is not
refracted at all. It will pass through in a straight line.
 If light moves from a less dense, to a more dense medium, the light bends towards the normal. (And vice versa.)
Snell’s Law
 When refraction occurs, the angle of incidence and the angle of refraction are related. This relationship was first
discovered by Snell (a Dutch scientist) and later by Descartes.
 This relationship, called Snell’s Law, is as follows:
o A ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of
refraction is a constant.
o This constant written as a ratio is known as the index of refraction.
n = sin i / sin R
Where: n = index of refraction of the second medium
i = angle of incidence
R = angle of refraction
o This equation ONLY works when light passes from air into some more dense medium.
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Snell’s Law is one of the two points of the LAWS OF REFRACTION:
1) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant (Snell’s Law)
2) The incident ray and the refracted ray are on opposite sides of the normal at the point of incidence, and all three
are in the same plane.
If light travels a medium other than air we must use the General Equation of Snell’s Law:
n1 sinΘ1 = n2 sinΘ2
Where: n1 = index of refraction for the incident medium
n2 = index of refraction for the refractive medium
Θ1 = angle of incidence
Θ2 = angle of refraction
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This general form of Snell’s Law can be used to solve any situation where’s Snell’s Law is to be used.
Lateral Displacement and Angular Deviation
 As light passes through a block of glass, it bends twice. If two refracting sides are parallel, the emergent ray is parallel
to the incident ray, however it is displaced. This sideways shifting is called lateral displacement.
Refraction Through a Triangular Prism
 When the glass block does not have parallel sides, the emergent ray takes a totally different path.
 The angle between the incident ray and the emergent ray is called the angle of deviation. This is the angular
displacement of the ray.
Dispersion
 When a beam of white light is allowed to pass through a prism each of the colored components of light undergoes a
separate amount of refraction to produce its own angle of deviation.
 The light comes out as a band of colors called a spectrum.
 This phenomenon is called dispersion.
 Any medium in which dispersion occurs is called a dispersive medium.
o Glass is an example of a dispersive medium
Total Internal Reflection
 As light passes from a medium with a high index of refraction to a lower index of refraction, light bends away from the
normal.
 As the size of the angle of incidence is increased, the size of the angle of refraction is also increased.
 Eventually the i value reaches a point where the R value reaches ninety degrees. The particular angle of incidence
that produces an angle of refraction of ninety degrees is called the critical angle (i c).
 If the i value is increased past the critical angle, the ray no longer refracts, but it reflects such that the angle of
incidence equals the angle of reflection.
 This phenomenon is called total internal reflection.
Condition for TIR
 There are two conditions needed for total internal reflection:
1) Light must be traveling from a medium with higher index of refraction to a medium of lower index of refraction.
2) The angle of incidence must be larger than the critical angle.
Critical Angle and Index of Refraction
 In order to determine the critical angle for two media, the following formula is used:
sin ic = n2 / n1
where: ic = critical angle
n1 = index of refraction of the incident medium
n2 = index of refraction of the refractive medium