SNELL’S LAW AND TOTAL INTERNAL REFLECTION
Lesson 8November 17th, 2010
SNELL’S LAW
The phenomenon of refraction had been observed for centuries, but it was not until 1621 that its cause was stated mathematically.
SNELL’S LAW
Willebrord Snell (1591–1626) was a Dutch astronomer and mathematician who is credited with identifying the exact relationship between the angle of incidence and the angle of refraction.
SNELL’S LAW
Snell’s law is a formula that uses values for the index of refraction to calculate the new angle that a ray will take as a beam of light strikes the interface between two media.
SNELL’S LAW
If you call the indices of refraction of the two media n1 and n2 and call the angles of incidence and the angle of refraction θ1 and θ2, then the formula for Snell’s law is:
n1sinθ1 = n2sinθ2
EXAMPLE 1 When light passes from air into water
at an angle of 60° from the normal, what is the angle of refraction?
G Index of refraction of air n1 = 1.00Index of refraction of water n2 = 1.33Angle of incidence Ѳ1 =
60°
S sinθ2 = 1.00 x sin60° 1.33
sinθ2 = 0.6511
θ2 = 40.62°R Angle of refraction = Ѳ2 P Therefore, the angle of
refraction is 41 degrees. A n1sinθ1 = n2sinθ2
sinθ2 = n1sinθ1
n2
EXAMPLE 2 In an experiment, a block of cubic zirconium is
placed in water. A laser beam is passed from the water through the cubic zirconium. The angle of incidence is 50°, and the angle of refraction is 27°. What is the index of refraction of the cubic zirconium?
G Index of refraction is 1.33Angle incidence Ѳ1 = 50°Angle of refraction Ѳ1 = 27°
S n2 = 1.33 x sin 50°sin 27°
= 2.244
R Index of refraction = n2 P Therefore, the index of refraction of the cubic zirconium is 2.2 A n1sinθ1 =
n2sinθ2
n2 = n1sinѲ1
sin Ѳ2
PRACTICE PROBLEMS 1
1. When light passes from air into water at an angle of 30° from the normal, what is the angle of refraction?
2. When light passes from water into diamond at an angle of 45° from the normal, what is the angle of refraction?
3. The refractive index of the lens in a human eye is 1.41. If a ray of light goes from the air into the lens at an angle of 55.0°, what is the angle of refraction?
PRACTICE PROBLEMS 2
1. A ray of light approaches a jar of honey at an angle of 30.0°. If the angle of refraction is 19.5°, what is the refractive index of honey?
2. A block of amber is placed in water, and a laser beam travels from the water through the amber. The angle of incidence is 35° while the angle of refraction is 24°. What is the index of refraction of amber?
3. A red laser beam travels from flint glass into lemon oil. The angle of incidence is
40.0° and the angle of refraction is 44.4°. What is the refractive index of lemon oil?
TOTAL INTERNAL REFLECTION
Sometimes, such as in the case of fibre optics, light does not pass from one medium to another but stays within the medium.
TOTAL INTERNAL REFLECTION
In total internal reflection, light reflects completely off the inside wall of a denser medium (higher index of refraction) rather than passing through the wall into a less dense medium (lower index of refraction).
TOTAL INTERNAL REFLECTION
Recall that when light passes from a denser material, such as water, into a less dense medium, such as air, the light refracts away from the normal.
TOTAL INTERNAL REFLECTION As the angle of incidence increases, the
angle of refraction increases. At a certain angle, called the critical angle, the refracted ray of light follows a path exactly along the surface of the water. Even though the light refracts, it does not leave the water. In a way, the light is “trapped” inside the water
TOTAL INTERNAL REFLECTION When light crosses a boundary
between materials with different indices, the light beam will be partially refracted at the boundary surface, and partially reflected.
MIRAGES
Both total internal reflection and refraction play a role in forming a mirage.
A mirage is an image of a distant object produced as light refracts through air of different densities.
MIRAGES
Since the light rays pass through layers of air with progressively lower indices of refraction, eventually the light is totally internally reflected.
INDEX OF REFRACTION - LAB