Diffraction

You will be able to Describe qualitatively double slit interference Solve problems involving diffraction gratings.

Interference Waves interfere (superposition) in a predictable way.

antinode Two crests meet: maximum displacement of the medium

node Where a crest meets a trough: complete destructive interference

Young discovered this in 1801

What Young proved!

The observed pattern has regular intervals that can be measured. Just like water waves

Diffraction of Red Light 102 103 Double slit Red filter Light diffracts Screen Po – central max P1 1st order image P2’ P1’ P0 P1 P2 Constructive interference Destructive Interference Antinode Node Bright band (fringe) Dark band

Monochromatic light’s wavelength can be calculated from the observed interference patterns using:

Example: Light is incident on a pair of slits 1.28 x 10-5 m apart. The maxima are 4.11 x 10-2 m apart and the screen is 1.00 m from the slits. What is the wavelength and colour of the light? See p. 676 for color

Solution

Solution

Example: Yellow monochromatic light, ʎ = 580 nm, shines on a pair of slits. The second dark spot is 21.8 cm from the central anti-node on a wall that is 5.00 m away. What is the slit separation?

Solution:

Solution:

Diffraction Gratings (interference gratings) Rather than a double slit to perform Young's experiment, multiple slits, called diffraction gratings, are more commonly used.

Diffraction Grating Transparent glass (or plastic) with opaque scratches placed very close together so it acts like multiple slits.

The bright maxima are much sharper and narrower for a grating than for a double slit, and, therefore, better for measuring wavelength.

The angle of diffraction depends on wavelength. If light of multiple wavelengths is used, the grating sorts out the wavelengths and produces a spectrum.

The formula for a diffraction grating is:

Review of Second Equation for Diffraction P2 P3 n=2 n=3 P0 P1’ Screen wavelength x d P1 Diffraction grating For angles less than 10⁰, the sine and tangent values are nearly equal

Eg) Light falls onto a diffraction grating ruled with 500 line /cm and casts a second order image at 2.00⁰. Determine the wavelength of light falling onto the grating in nanometers.

Eg 2) Light falls on a pair of slits 1. 35 um apart Eg 2) Light falls on a pair of slits 1.35 um apart. The maxima are measured to be 41.0 cm apart and the screen is a distance of 1.00 m from the slits. Determine the wavelength of light using each diffraction equation: