Fluids, Thermodynamics, Waves, & Optics Optics Lab 9 Interference and Diffraction

Transcription

1 Fluids, Thermodynamics, Waves, & Optics Optics Lab 9 Interference and Diffraction Lana Sheridan De Anza College Jun 13, 2018

2 Overview Purpose Theory interference from two coherent light sources diffraction from a single light source interference and diffraction Part 1: Single slit diffraction Part 2: Two slit interference with diffraction

3 Purpose of the Lab To investigate the wave nature of light. You will use a laser on an optical bench and screens to study diffraction and interference patterns. You will 1 observe a single slit diffraction pattern and calculate the slit width from the observed pattern. 2 observe a two-slit pattern and calculate the slit separation and slit widths.

4 Equipment

5 Interference of Light 37 Wave Optics e slits s on es Constructive interference occurs at point O when the waves combine. Constructive interference also occurs at point P. Destructive interference occurs at point R when the two waves combine because the lower wave falls one-half a wavelength behind the upper wave. S 1 S 2 Bright O fringe S 1 S 2 P O Bright fringe S 1 S 2 P R Dark fringe O Viewing screen a b In places where the path lengths differ by a whole number of wavelengths (mλ) there is constructive interference. the upper one by exactly one wavelength, they still arrive in phase at P and a second bright fringe appears at this location. At point R in Figure 37.3c, however, between points O and P, the lower wave has fallen half a wavelength behind the upper wave and a crest of the upper wave overlaps a trough of the lower wave, giving rise to destructive interference at point R. A dark fringe is therefore observed at this 1 Serway location. & Jewett. c

6 Interference A pattern of light and dark fringes (stripes of light and darkness) appear on the screen. Zoomed in view:

7 37.5b), which is approximately true if L is much greater than d, then d is given by Interference: Finding the Maxima d 5 r 2 2 r 1 5 d sin u (37.1) The For value a distant of d determines screen and whether closely the placed two waves slits, are the in phase two rays when are they nearly arrive at point parallel. P. If d is either zero or some integer multiple of the wavelength, the two waves P r 1 r 1 S 1 y S 1 r 2 d Q S 2 u u r 2 d u O d S 2 d r 2 r 1 d sin u L Viewing screen When we assume r 1 is parallel to r 2, the path difference between the two rays is r 2 r 1 d sin u. a Looking at the right triangle with hypotenuse d (the slit separation distance): δ = d sin θ. b

8 Interference: Finding the Angles of the Maxima Maxima (bright fringes) occur when d sin θ max = m i λ where m i Z Minima (dark fringes) occur when d sin θ min = ( m i + 1 ) λ 2 where m i Z These expressions give us the angles (measured outward from the axis that passes through the midpoint of the slits) where the bright and dark fringes occur.

9 ence d (Greek letter delta). If we assume the rays labeled r 1 and r 2 ar 37.5b), which is approximately true if L is much greater than d, then d Young s Experiment: Finding the Position of the Maxima d 5 r 2 2 r 1 5 d sin u We canthe alsovalue predict of d the determines distance whether from the center two of waves the are screen, in phase y, when in terms point of the P. If distance d either from zero the or slits some tointeger the screen, multiple L. of the wavelength P r r 1 S 1 y S 1 d Q r 2 u u u d O S 2 d S 2 d r 2 r 1 tan θ = y L sin θ L Viewing screen if θ is small When we assum parallel to r 2, th difference betwe rays is r 2 r 1

10 Interference: Finding the Angles of the Maxima Maxima (bright fringes) occur when y is such that: d = m i λ L y where m i Z Minima (dark fringes) occur when y is such that: d = ( mi + 1 ) 2 λ L y where m i Z These expressions give us the angles (measured outward from the axis that passes through the midpoint of the slits) where the bright and dark fringes occur.

11 alternating with dark fringes. Diffraction: Intensity Pattern from a Single Slit Incoming wave Slit min max min u max min max L min Viewing screen a b

12 Dividin right of th Diffraction: Understanding Each portion of the slit Single acts as Slit Pattern difference Consider a series ofa point sources inof different light waves. parts of the slit. between The r slit has width a. difference the pairs o 5 lation occu 4 because th the upper a a/2 a/2 u a sin u or, if we c below,

13 Diffraction: Understanding the Single Slit Pattern We can find minima (dark fringes) in the pattern by breaking up our point sources into pairs that cancel each other out. Matching point sources in the top half of the slit with ones in the bottom half, the source separation distances will be d = a/2. This will be a fringe dark when: δ = a 2 sin θ = λ 2

14 Diffraction: Understanding the Single Slit Pattern However, we could also break the slit up into 4 equal parts and match sources from the 1st and 2nd, and match from the 3rd and 4th. This will be dark when: δ = a 4 sin θ = λ 2 If we break the slit up into 6 equal parts and match sources from the 1st and 2nd, the 3rd and 4th, and the 5th and 6th. This will be dark when: δ = a 6 sin θ = λ 2

15 Diffraction Minima In general we expect dark fringes when: or, equivalently, sin θ min = m d λ a a sin θ min = m d λ where m d = ±1, ±2, ±3,...

16 Interference AND Diffraction: Two slits that have some width Suppose two slits each have width a and their centers are a distance d apart. What intensity pattern do they create?

17 Interference AND Diffraction: Two slits that have 38.2 Diffraction Patterns from some width In the picture, d/a = 6 Interference fringes Diffraction minima I The diffraction pattern acts as an envelope (the blue dashed curve) that controls the intensity of the regularly spaced interference maxima. F e i d p a 3p 2p p p 2p 3p p a sin u l

18 Equipment: Setup

19 Diffraction Pattern Measurement Figure: For demonstration only! Measure the distances from the pattern copied into your lab book, so that you do not accidentally scatter the laser off of the calipers and into your eyes.

20 Interference and Diffraction Pattern

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