Ch. 22  Reflection and Refraction of Light

 

22.1 The Nature of Light (Read!)

 

Although we often talk about light as being an electromagnetic wave, in many experiments it behaves as a particle (as Newton originally thought it was). Most notably, the emission of hot condensed objects was at odds with standard electromagnetic theory, as was the photoelectric effect. However, both could be explained if light behaved as a particle with an energy proportional to its equivalent frequency:

 

where h is Planck’s constant. For a more lengthy discussion (if you want it) visit a chapter from my Physics of Light & Color class here.

 

Depending on how the experiment is done, sometimes light behaves as a wave, and sometimes it behaves as a particle  “wave-particle duality”.

 

22.2 The Ray Approximation in Geometrical Optics

 

 

 

Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different materials. We approximate the motion of plane waves using rays oriented perpendicular to the wave fronts.

 

 

22.3 Reflection and Refraction

 

REFLECTION

 

It has been known for a couple thousand years that light reflecting off of a smooth shiny object does so following a simple rule: The angle of reflection with respect to the normal to the surface equals the angle of incidence:

 

 

 

 

In those early days, a mirror was referred to as a speculum (you might still hear it called this in certain fields), so that we use the term specular reflection for this process. In contrast, rough surfaces produce diffuse reflection or scattering.

 

(a) specular reflection

(b) diffuse reflection

 

 Unless otherwise noted, we will use “reflection” to mean “specular reflection”.

 

Example 22.1 The Double-Reflected Light Ray

 

Two mirrors make an angle of 120° with each other. A ray is incident on mirror M1 at an angle of 65° to the normal. Find the angle the ray makes with the normal of M2 after it is reflected by both mirrors.

 

REFRACTION

 

When light hits a transparent medium, part of it usually travels into the medium, but with a change in direction.

 

 

The ray that gets bent and travels through the medium is said to be refracted, and the process is called refraction. Note that the incident ray, refracted ray, and reflected ray all lie in the same plane, normal to the surface of the interface of the two media.

 

 

 

 

 

The change in direction of the refracted rays result from the fact that the speed of light in a medium depends on the nature of the medium. This results in an angle of refraction that is related to the angle of incidence:

 

 

 

This will be then first form of the relation called Snell’s Law, after the person who discovered it.

 

 

The light gets bent toward the normal when slowing down, and away from the normal when speeding up.

 

Note: these light paths are reversible! They are equally valid with the rays pointing the other way.

 

22.4 The Law of Refraction

Index of Refraction       

 

When light passes from one medium into another the frequency f remains constant (or else waves would have to be selectively created or destroyed). So if v changes and f is constant, then λ must also change, since .

 

 

Finally:

 

 

This will be the form of Snell’s Law of Refraction that we will usually use.

The index or refraction varies from material to material, It will also depend on the wavelength of the light itself:

 

 

Example: Problem #15

 

A beam of light, traveling in air, strikes the surface of mineral oil at an angle of 23.1° with the normal to the surface. If the light travels at 2.17 x 108 m/s through the oil, what is the angle of refraction?

 

Example: Quick Quiz 3

A material has an index of refraction that increases continuously from top to bottom. Of the three paths shown, which path will the light ray follow as it passes through the material?

 

22.5 Dispersion and Prisms

 

 

 

 

 

The index of refraction n depends on the wavelength λ of the light. Usually (but not always) n increases as λ decreases. This  process is called dispersion. (Actually this is normal dispersion  in those cases where n increases as λ increases we have anomalous dispersion).

 

 

So when light composed of more than a single wavelength crosses from one medium into another, different wavelengths get bent by different amounts, and the different wavelength get separated or dispersed from one another.

When light passes through a prism, the angle of deviation δ is different for the different wavelengths. This property can be put to use in the form of a prism spectrometer:

 

Every element has its own “fingerprint” in the wavelengths of light it emits or absorbs. This can be used to analyze the composition of atoms & molecules in the lab, the field, or across the universe.