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