Diffraction of Light Concepts

Study Notes

Diffraction of Light

Diffraction refers to the bending of light rays around sharp edges, allowing light to enter areas that would otherwise be in shadow.
This phenomenon is explained by the wave nature of light and is based on Huygen’s theory.

Fraunhofer Diffraction at Single Slit

Key path difference for two rays diffracted at angle θ is given by ( x = a \sin \theta ).
Dark fringes occur when the path difference equals ( \lambda ) or its integral multiple, altering the conditions for bright and dark fringes.
For bright fringes, the equation is ( a \sin \theta_n = \frac{(2n+1) \lambda}{2} ).
For dark fringes, the condition is ( a \sin \theta_m = m \lambda ).

Fraunhofer Diffraction at Double Slit

Intensity distribution on the screen results from both diffraction and interference:
- Individual slit diffraction patterns that overlap.
- Interference patterns from superposition of rays from two slits.

Diffraction Pattern

Bright fringes for single slits follow: ( a \sin \theta_n = \frac{(2n+1) \lambda}{2} ).
Dark fringes maintain: ( a \sin \theta_m = m \lambda ).

Interference Pattern

Path difference for rays at angle θ is: ( x = (a + b) \sin \theta ).
For nth order interference maximum: ( (a + b) \sin \theta_n = n \lambda ).
For nth order interference minimum: ( (a + b) \sin \theta_n = \frac{(2n+1) \lambda}{2} ).

Missing Orders of Interference

Interference maxima occurring at the same angular position as diffraction minima results in absence of those fringes.
Equations depict the condition:
- ( (a + b) \sin \theta = n \lambda ) for maximum.
- ( a \sin \theta = m \lambda ) for minimum.
Dividing leads to ( \frac{a + b}{a} = \frac{n}{m} ), showing relationships:
- If ( a = b ): ( n = 2m ) — even orders of interference are missing.
- If ( 2a = b ): ( n = 3m ) — multiples of three are missing.
- If ( b = 0 ): all interference fringes are absent.

Intensity Distribution on Screen

The resulting intensity distribution combines the interference pattern within the diffraction fringes.

Diffraction Grating/Plane Transmission Grating

A diffraction grating consists of numerous parallel slits with equal spacing and widths, separated by opaque regions.
Constructed by ruling lines with a fine diamond point on a glass plate, typically containing 12,000 to 30,000 lines per inch.
Each slit has a width ( a ) (transparent) and opaque portions have width ( b ).
Grating constant is ( a + b ), with its reciprocal defining the number of lines per unit length on the grating.

Description

This quiz covers the intricate phenomena of light diffraction, focusing on the bending of light rays around sharp edges and how they enter shadow regions. It emphasizes understanding through Huygen’s theory and explores the Fraunhofer diffraction at a single slit.