Core Unit III: Light
C. Refraction

1. Snell's Law

Key Concepts

Refraction is the bending of light that takes place at a boundary between two materials having different indices of refraction. Refraction is due to a change in the speed of light as it passes from one medium to another.

The boundary is the region where one medium meets another medium .

At a boundary, an incident ray can undergo partial reflection or, in certain situations, total internal reflection.

No bending of the incident ray occurs if it strikes the boundary along the normal.

The incident ray is the ray approaching the boundary. It strikes the boundary at the point of incidence. The refracted ray is the ray leaving the boundary through the second medium.

The reflected ray is the ray undergoing partial (or total) reflection at the boundary. The normal is a construction line drawn perpendicular to the boundary at the point of incidence.

The angle of incidence (i) is the angle between the incident ray and the normal. The angle of reflection (r) is the angle between the normal and the reflected ray.

The angle of refraction (R) is the angle between the normal and the refracted ray.

Both Reflection and Refraction occur when the light is incident on a more refractive medium.

Some texts use the symbol r for the angle of refraction. The use of the same symbol to represent both the angle of reflection and the angle of refraction can be very confusing and should be avoided.

Laws of Refraction:

1. The ratio of sines of the angles of incidence and refraction is a constant. (Snell's Law) (The ratio is constant for a particular wavelength and a particular set of materials.)

2. The incident and refracted rays are on opposite sides of the normal at the point of incidence.

3. The incident ray, the normal, and the refracted ray are coplanar.

the constant is the ratio of the speeds of light in the two media.)

General form:

or, n₁sin₁ = n₂sin₂

(The absolute index of refraction for a given medium is defined as: n = c/v where c is the speed of light in a vacuum and v is the speed of light in the medium. Also, the ratio n₂/n₁ is called the relative index of refraction.)

Subscript 1 is customarily used to represent the incident medium. Subscript 2 epresents the refractive medium. The equation is valid regardless of the direction in which light is travelling through the two media. (i.e., The Principle of Reversibility applies).

If light is travelling from a less refractive medium to a more refractive medium (i.e., n₂ > n₁), the refracted ray will be bent towards the normal.

The term optical density, as is sometimes used, is misleading and should be avoided. There is no relationship between the mass density of a medium and its optical density. For example, benzene and corn oil, which both float on water, have higher refractive indices than water. Optical density refers to the transparency of the medium and has nothing to do with its refractive index.

Newton's experiments illustrated the dispersion of sunlight into a spectrum (and recombination into white light). Sunlight consists of amixture of light with different wavelengths. A dispersive medium is one in which different wavelengths of light have slightly different indices of refraction. For example, crown glass is a dispersive medium since the index of refraction for violet light in crown glass is higher than for red light. This is responsible for chromatic aberration. (Manufacturers of optical glass customarily specify the refractive index of a material for yellow sodium light, the D line.)

Light passing through a rectangular prism can experience lateral displacement. In a prism with non-parallel sides, the displacement is described by the angle of deviation between the ray incident to the prism and the ray emerging from it.

Many examples found in commonly observed phenomena and practical applications illustrate refraction and total internal reflection. (Several should be described and discussed or researched independently by students.)

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: refraction, boundary, partial reflection, point of incidence, refracted ray, angle of refraction, spectrum, dispersion, dispersive medium, chromatic aberration, lateral displacement, angle of deviation.

2. Explain why refraction occurs.

3. Explain that no bending of the incident ray occurs if it strikes the boundary while travelling along the normal.

4. Draw and label a diagram which illustrates the way in which light behaves when it undergoes refraction.

5. State the three laws of refraction.

6. Apply Snell's Law to solve problems relating to refraction.

7. Recognize the direction that a refracted light ray will bend, depending on the relative index of refraction for the two media.

8. Explain what causes chromatic aberration.

9. Solve problems relating to the refraction of light.

10. Identify several applications or examples from common experience which illustrate the refraction of light .

Teaching Suggestions, Activities and Demonstrations

1. Perform an activity to investigate the refraction of light.

2. Illustrate experimentally that when sunlight enters a dispersive medium, such as a prism, dispersion occurs.

3. Explain or demonstrate the experimental techniques that Newton used to investigate the dispersion and subsequent recombination of sunlight by a prism.

4. Perform an activity to investigate the lateral displacement of light through a rectangular prism.

5. Using a glass equilateral prism, or some other apparatus, determine the index of refraction for one type of glass, or some other medium.

6. Design an experiment to determine the index of refraction of a variety of transparent solid or liquid substances. Some students may be able to build small transparent plexiglass cubes and prisms that can be filled with different types of transparent fluids to investigate refraction.

7. Design an experiment to investigate the concentration of a sugar solution and its index of refraction.

8. Slowly pour water containing a colloidal suspension over a layer of sugar crystals in the bottom of an aquarium, trying not to allow too much turbulence to develop in the water. Allow a concentration gradient to form in the sugar solution. Predict what will happen when a beam of light shines through the solution. Shine a beam through the solution. Account for the curved path that the beam follows in the liquid.

9. A laser beam provides an excellent source of light for various optics demonstrations. Modern technology has reduced both the size and the cost of this light source. Consider purchasing one for the science lab, if one is not currently available.