Young’s Double Slit Experiment

Light as a Wave? If light behaves like a wave, an experiment

similar to a ripple tank using two light sources should reveal bright areas (constructive interference) and dark areas (destructive interference) on a screen. However, researchers could not detect it until …

Thomas Young’s Experiment in 1803

Young’s Double Slit Experiment What is light? Veritasium Video: http://www.youtube.com/watch?v=Iuv6hY6zsd0

http://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Doubleslit.gif/220px-Doubleslit.gif

Young’s Double Slit Experiment Thomas Young devised

an ingenious experiment that

produced an interference

pattern with light.

Using a natural

light source, Young

allowed the light

to fall onto an opaque

material with a single,

narrow slit.

Young’s Double Slit Experiment The light passing through

the single slit diffracted and

spread as it travelled to a

second opaque barrier that

had two narrow slits placed

very close together. Therefore

the light leaving the double

slits acted as 2 sources and was

essentially coherent or in phase.

Young’s Double Slit Experiment The light that passed through the double-slit barrier fell on

a nearby screen, producing the historic pattern of light and dark lines caused by the interference of light waves.

The bands of bright and dark are called interference fringes or maxima and minima respectively.

This was the evidence of the wave nature of light that scientists had been looking for!

Analyzing Light Interference The bright and dark fringes are alternating

regions of constructive interference (CI) and destructive interference (DI).

To analyze the interference, we need to determine the path length difference between each slit and the screen.

Analyzing Light Interference To simplify the analysis, we assume that:

• 1. The screen is a long way from the slits so L >> d; P → ∞

• 2. Since L >> d, the path lengths L1 and L2 are nearly parallel

• 3. Since L1 and L2 are parallel, the angles of the path lengths L1 and L2 from each of the slits to point P on the screen are approximately equal (𝜃 = 𝜃′)

• 4. The wavelength 𝝀 is much smaller than d

path difference

path difference = ∆𝐿 = dsinθ

Analyzing Light Interference

Analyzing Light Interference From the path difference between the 2 sources:

Constructive interference occurs when the light waves are in phase and the light from each source travels the same distance to reach the screen

Bright bands or maxima occur at:

𝑠𝑖𝑛𝜃𝑚 =m𝝀

𝑑

where m = 0,1,2,3,… are the maximum numbers called zero-order maximum, first-order maximum, etc.

Analyzing Light Interference Destructive interference occurs when the light waves

are out of phase and the light from one source travels

an extra distance of 𝝀2 to reach the screen.

Dark bands or minima occur at:

𝑠𝑖𝑛𝜃𝑛 = 𝑛 −1

2

𝝀

𝑑

where n = 1,2,3,… are the nodal line numbers called first-order minimum, second-order minimum, etc.

Analyzing Light Interference From the diagram, to calculate the fringe width:

𝑥

𝑛

𝐿= 𝑡𝑎𝑛𝜃𝑛 but as L ≫ x, tanθ ~ sinθ so

𝑠𝑖𝑛 𝜃𝑛 = 𝑥𝑛

𝐿= 𝑛 −

1

2

𝝀 𝑑

such that

𝑥𝑚 = 𝑚𝐿𝝀

𝑑 for the mth-order bright fringe width.

𝑥𝑛 = 𝑛 −1

2

𝐿𝝀

𝑑

for the nth order dark fringe width.

Note: The fringe width and

intensity of the bright fringes is uniform

Analyzing Light Interference To calculate the separation between any

2 adjacent fringes:

∆𝑥 = 𝐿𝝀

𝑑

where

∆𝑥 is the distance between adjacent

nodal lines on the screen

d is the separation of the slits

L is the perpendicular distance

from the slits to the screen

Note: The central fringe (zero-order max.) = 2x1

Some Light Work Example 1: Imagine you are Thomas Young measuring

the wavelength of light from a certain single-colour source. You direct the light first through a single slit which diffracts to two slits with a separation of 0.15 mm, and an interference pattern is created on a screen 3.0 m away. You find the distance between the first and eighth consecutive dark lines to be 8.0 cm. At what wavelength is your source radiating?

Example 2: The third-order dark fringe of 652 nm light is observed at an angle of 15.0° when the light falls on two narrow slits. How far apart are the slits?