Wave Optics

## Big Picture

Visible light is one type of electromagnetic (EM) radiation and only represents a tiny portion of the whole EM spectrum. All electromagnetic radiation is transferred by waves that can interact with each other. Wave optics mainly has to do with the how these waves will interfere with each other. While we modeled light as rays in geometric optics, we will be dealing with how light behaves as a wave in this study guide.

## Key Terms

Amplitude: In wave optics, the amplitude of an electromagnetic wave is the intensity of the wave.

Interference: When two waves of the same type meet, they combine to create a larger or smaller wave. For more information on interference, see the Waves study guide.

Interference Pattern: Pattern resulting from interference. Light interference patterns are alternating light (minima) and dark bands (maxima).

Diffraction: Occurs when a wave hits an obstacle or a barrier.

Fresnel Diffraction: An approximation that can be used to estimate propagation of waves when very close to an antenna emitting electromagnetic waves.

Fraunhoffer Diffraction: An approximation that can be used to estimate the propagation of waves when very far from an antenna emitting electromagnetic waves.

Resolving Power: The ability of a device to distinguish between different wavelengths in the electromagnetic spectrum.

Doppler Effect: Describes an apparent change in wavelength because of the relative motion of the source of a wave and an observer.

## Light as a Wave

Light has a dual nature:

• In some situations, it is better to model light as particles called photons.
• In other situations, it is better to model light as a wave. Light waves are electromagnetic waves, which contain changing electric and magnetic fields that are oriented in directions perpendicular to the direction of travel.

Electromagnetic radiation is categorized by its wavelength, ranging from radio waves of wavelength $$10^8$$ meters to gamma rays of wavelength $$10^{-16}$$ meters. Below is an illustration showing the divisions in the electromagnetic spectrum. Image Credit: Philip Ronan, CC-BY-SA 2.5

In the case of visible light, the brightness of the light corresponds to the amplitude of the wave.

## Physics

Wave Optics cont.

## Interference

Electromagnetic waves can interfere constructively or destructively just like any other type of wave. However, it is possible to create easily visible interference patterns with light (unlike other types of waves such as sound).

Interference patterns are created any time that two light waves with the same wavelength reach the same point by traveling along slightly different paths. If we observe the light waves interacting on a surface such as a screen or a wall, there will be places where the interference pattern is bright (constructive interference) and places where the pattern is dark (destructive interferences). There are many situations where this is possible, including when light passes through a thin film or multiple separated slits.

### Michelson Interferometer

The interferometer are used to split beams of light into different paths and then recombine them to create an interference pattern. Michelson used his design for an interferometer to demonstrate how the speed of light remained constant in an accelerating reference frame.

## Interference (cont.)

### Thin Film Interference

When there is a thin layer of a transparent substance on top of another material, some of the incident light will be reflected off the top of the surface and some will refract through the layer and then reflect off the bottom of the layer. The two rays of light traveled a different distance and will create an interference pattern when both rays emerge from the thin layer.

To the right is a diagram that shows the path of the light waves in the thin film.

The colors in soap bubbles are the result of thin film interference. The different colors reflect the thickness of the bubble. Image Credit: Chanli44, Public Domain

## Diffraction

Light, like other waves, demonstrates diffraction. It is most noticeable when the wavelength of the wave is similar to the size of the obstacle.

### Single Slit Diffraction

Passing light through a slit that is of comparable size to the wavelength will create an interference pattern. This can be explained by thinking of all the points in the opening as a point source for waves. The diffraction pattern will fall off in brightness very quickly from the central maxima. To the right is a diagram showing a single slit diffraction. Image Credit: Dicklyon, Public Domain

### Double Slit Diffraction

Double slit diffraction occurs when passing light through two slits separated by a small distance. The interference pattern is the result of the light waves from the two slits being slightly out of phase when they hit surface after traveling slightly different distances. The double slit experiment was used to prove that light is a wave. To the left is a diagram of an arrangement that would cause double slit diffraction. Image Credit: Inkwina, Public Domain

### Multiple Slit Diffraction

Multiple slit diffraction is very similar to double slit diffraction and creates a similar interference pattern, except the brightness will not decrease as fast from the central maxima.

## Physics

Wave Optics cont.

## Doppler Effect

Like sound waves, electromagnetic waves such as light experiences the Doppler effect. There are some special terms associated with the Doppler effect for light.

• Red Shift: Occurs when objects are moving away from each other, which increases the wavelength. It is called red shift because the emitted light shifts toward the red end of the visible spectrum.
• Blue Shift: Occurs when object’s are moving toward each other, which decreases the wavelength.

## Important Equations

Note: substitute $$(n + \frac{1}{2})$$ for n when trying to find a minima instead of a maxima. Also, the third equation uses the approximation that $$\sin \theta \approx \tan \theta = \frac{x_m}{L}$$ for small angles.

$$c= \lambda f$$

c - speed of light

λ - wavelength

f - frequency

$$d = \sin \theta = n \lambda$$

d - separation of slits

θ - angular position of maxima/minima

n - number of maxima/minima from central maxima

$$\frac{dx_m}{L} = n \lambda$$

$$x_m$$ - distance from central maxima

L - distance to screen