Young s Double Slit Experiment

Transcription

1 Young s Double Slit Experiment

2 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

3 Young s Double Slit Experiment What is light? Veritasium Video: eslit.gif/220px-doubleslit.gif

4 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.

5 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.

6 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!

7 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.

8 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

9 Analyzing Light Interference

10 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: sinθ m = mλ d where m = 0,1,2,3, are the maximum numbers called zero-order maximum, first-order maximum, etc.

11 Analyzing Light Interference Destructive interference occurs when the light waves are out of phase and the light from one source travels an extra distance, a multiple of λ 2 Dark bands or minima occur at:, to reach the screen. sinθ n = n 1 2 λ d where n = 1,2,3, are the nodal line numbers called first-order minimum, second-order minimum, etc.

12 Analyzing Light Interference From the diagram, to calculate the fringe width: x n L = tanθ n but as L x, tanθ ~ sinθ so sin θ n = x n L = n 1 2 x m L = mλ d x n L = n 1 2 λ d such that for the m th order bright fringe width. λ d for the n th order dark fringe width. Note: The fringe width and intensity of the fringes is uniform

13 Analyzing Light Interference To calculate the separation between any 2 adjacent fringes: where x L = λ d 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.) = 2x 1

14 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?