Wave Optics: Diffraction and Interference

Study Notes

Wave optics describes the wave-like behavior of light, including interference and diffraction.
The geometric path refers to the actual distance traveled by light, while the optical path length is the product of the geometric path length and the refractive index of the medium.

Diffraction is the bending or spreading of light waves as they pass through an aperture or around sharp edges of objects.
Single-slit diffraction occurs when light passes through a single slit whose width is comparable to the wavelength of light.

Interference is the superposition of two or more waves, resulting in a resultant wave with a greater, lower, or the same amplitude.
Constructive interference occurs when crests of waves meet, resulting in an amplitude equal to the sum of the individual amplitudes.
Destructive interference occurs when a crest meets a trough, resulting in a difference in amplitude.
The phase difference between two waves can change if they travel through different materials with different refractive indices.
The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in the medium.

Overlapping waves algebraically add to produce a resultant wave (or net wave).
Two waves traveling in opposite directions along a stretched string experience superposition as they move through each other.
Overlapping waves do not alter the travel of each other.

A diffraction grating is a device consisting of a large number of parallel, closely spaced slits.
The grating equation relates the angle of diffraction (θ), the wavelength of light (λ), the grating spacing (d), and the order of the interference maximum (m): mλ = d sin(θ)

The resolving power of a diffraction grating is its ability to distinguish between two closely spaced wavelengths.
The resolving power is given by the product of the number of lines (N) on the grating and the order of the interference maximum (m): R = Nm

Newton's rings are a phenomenon of interference observed when a plano-convex lens is placed on a reflecting surface (like a flat glass plate).
The interference occurs between the light reflected from the top and bottom surfaces of the air film between the lens and the plate.

The diameter of the bright rings is given by: D_n²= 4nRλ
- Where: n is the order of the bright ring, R is the radius of curvature of the lens, and λ is the wavelength of light.
The diameter of the dark rings is given by: D_n²= 4(n-1/2)Rλ

The wavelength of monochromatic light can be measured using Newton's rings by measuring the diameter of the rings.
The wavelength is calculated using the formula: λ = D_n² / 4nR

Interference effects are used in anti-reflecting coatings for lenses and other optical devices.
These coatings typically consist of thin films with a refractive index lower than that of the lens material.
By adjusting the thickness of the film, destructive interference can be achieved for specific wavelengths of light, reducing reflection and improving transmission through the lens.