Measuring a Human Hair

Interference is a property of wave interaction. The presence of interference in the propagation of light is a strong argument for it being a wave.

Using a laser, it is possible to observe interference when it is projected past a human hair. A picture of the experimental set up follows.

The note card in the picture has had a hole punched in it, and a human hair is suspended across the hole and held in place by tape. A laser is aimed past the hair so that the beam is bisected by it. On the recieving surface, it is possible to observe interference effects, though this photo did not capture them. This is due to the low intensity of the constructive interference bands.

By measuring the distance from the notecard to the flat surface, the distance from the center of the laser beam to the center of one of the intensity peaks, and using the wavelength of the laser, it is possible to measure the diameter of the hair suspended in the notecard.

Our experiment generated the following results

Length from notecard to board : 2 meters
distance from laser center to 3rd anti-node (Ym): 6.5 cm

wavelength of light emitted: 630 - 680 nanometers

using the constructive interference approximation equation
Ym = Length * wavelength * anti-node number / diameter of hair

Solving this equation for diameter results in a range of diameters from 5.85*10^-5 meters to 6.27*10^-5 meters. Upon further investigation, a microscope determined that the diameter of the hair was approximately 6*10^-5 meters which supported the laser measurement.

Thin Lens experiment

As always, the data for this experiment can be found on google documents by following this link.

A magnifying lens can be modelled as a thin lens in the physics of optics because its total thickness is negligible in comparison to the radius of curvature for each surface.

For this experiment we used a light box, a paper with a non symmetric cross printed on it, a magnifying lens, and a flat surface to project the image on.

The above image shows the light box and lens combination.
When the ambient lighting is suppressed and the light box is projected through the lens, an inverted image can be seen on the opposite side of the lens.

Though barely visible in the glass, it is possible to see that the reflection of the cross is both vertically and horizontally inverted from the image that appears on the flat box.

The sharpness and size of the projected image was found to be variant with light box distance (object distance) and projected surface distance (image distance). Both measurements are in reference to the center of the lens.

In order to collect data, the light box was placed at a known distance, and the flat surface was moved until a sharp image was formed. The two relative distances were recorded and put into a table. The plot of Image distance vs. object distance follows.

It appears to have a relationship which approximates a reciprocal, however, a plot of their inverses, when summed provides a more thorough explanation.

It is apparent from this graph that the summation of the reciprocal of the two values is nearly constant. Further investigation reveals that the average value for this summation is approximately 1/focal length.

Geometric approach to optics

In the study of electromagnetic wave propagation, a simplification to geometric rays can aid understanding.
For example, when dealing with the subject of the appearance of an object when viewed in a convex mirror can be simplified to the 2 dimensional case, as it appears in the following image.

The trajectory of 3 rays originating at the top of the object is illustrated. The point at which those three rays converge, is the reflected image location. In this case, the image is smaller and inverted. It can be shown with additional rays that the reflected image acts as its own point source and is thus a real image.