Overview
This lecture focuses on the formulas and calculations involved in interference and diffraction of light, including fringe spacing, wavelength, and related numerical examples.
Interference and Diffraction Basics
- Double-slit interference produces bright and dark fringes due to constructive and destructive interference.
- The position of bright fringes (maxima) is given by (a \sin \theta = n \lambda), where (n) is an integer.
- The position of dark fringes (minima) is given by (a \sin \theta = (2n-1)\lambda/2).
- Fringe spacing ((\Delta x)) is calculated using (\Delta x = \lambda D / a), where (D) is the screen distance, (a) is slit separation, and (\lambda) is wavelength.
Key Formulas and Example Calculations
- Convert wavelength units: 1 angstrom = (10^{-10}) meters.
- For example, (\lambda = 5890 \times 10^{-10}) m, (a = 1 \times 10^{-3}) m, (D = 1.5) m, so (\Delta x = 8.835 \times 10^{-3}) m.
- For various media, the effective wavelength is (\lambda_{med} = \lambda_{air} / \mu), where (\mu) is the refractive index.
- Changes in fringe width when air is replaced by another medium can be found by (\Delta x_{air} - \Delta x_{med}).
- Maximum value of (\sin \theta) is 1, corresponding to (\theta = 90^\circ).
- For single-slit diffraction, minima occur at (a \sin \theta = n \lambda).
Grating and More Examples
- For diffraction grating, the formula is (d \sin\theta = n\lambda), where (d) is the grating spacing.
- Largest value of (n) is found by (n_{max} = d / \lambda).
- For wavelength change in different substances, (\lambda' = \lambda / \mu).
- For circular fringes and maxima or minima, count using appropriate 'n' values._
Key Terms & Definitions
- Fringe Spacing ((\Delta x)) — Distance between adjacent bright (or dark) fringes in interference.
- Wavelength ((\lambda)) — The distance between two consecutive peaks in a wave.
- Path Difference — The difference in distance traveled by two waves from source to point of interest.
- Refractive Index ((\mu)) — Ratio of speed of light in vacuum to that in the medium.
- Diffraction Grating — An optical component with a regular pattern that splits light into several beams.
Action Items / Next Steps
- Review formulas for interference and diffraction, especially for fringe width and maxima/minima conditions.
- Complete assigned problems involving calculation of fringe spacing and effect of medium change.
- Prepare for questions involving conversion between units (angstroms to meters) and substitution in formulas.