Physics 202, Lecture 28

Transcription

1 Physics 202, Lecture 28 Today s Topics Michelson Interferometer iffraction Single Slit iffraction Multi-Slit Interference iffraction on Circular Apertures The Rayleigh Criterion Wave Superposition Using Phasors 1

2 Michelson Interferometer Very sensitive method for measuring small changes in path length differences and/or small change in speed of light propagation 2

3 Single-Slit iffraction If lights were just rays 3

4 Δy E 0 y Single-Slit iffraction Pattern Explained The slit is not a point source Interference E p = E i θ φ(ψ)=2π/λ ysinθ = ( Δy E 0 )sin(ωt + 2π λ ysinθ) = = /2 /2 E 0 2E 0 sin(ωt + 2π λ ysinθ)dy 2π λ sinθ sin( 2π λ 2 sinθ)sin(ωt) sin(β /2) I = I 0 β /2 2 The text also offers a derivation using phasors. Not on exam, but please read. β 2π λ sinθ 4

5 Single Slit iffraction: Where Are the ark Fringes? sin(β /2) I = I 0 β /2 β 2π λ sinθ 2 The dark fringes occur at : I=0 sin(β/2)=0 sinθ dark =mλ/, m=± 1, ± 2, ± 3,... 5

6 Summary: Single-slit iffraction sin(β /2) I = I 0 β /2 2 Separation between minima = λ β 2π λ sinθ

7 Reminder: Two-slit Interference path length difference δ =dsinθ ~ dθ ~ d y/l Separation between minima = λ d πd sinθ I = I o cos 2 λ

8 sin(β /2) I = I 0 β /2 2 Two-slit iffraction β 2π λ sinθ δ I = I o cos 2 2 δ = 2π λ dsinθ sin(β /2) I = I 0 β /2 2 δ cos 2 2

9 Multi-Slit Interference N slits # secondary maxima = N -2 Higher N more suppression of secondary minima (Grating: N>1000, highly sensitive to λ, good for measuring λ. 9

10 iffraction on Circular Apertures Light through apertures will produce diffractive patters depending on their shape. For circular apertures the diffractive patters is made of concentric rings Separation between minima = 1.22 λ

11 Resolution of Single-slit and Circular Apparatus two separate beams each smeared due to diffraction Rayleigh s Criterion Separable Minimally separable Not separable Single slit: θ min = λ/ Circular opening: θ min = 1.22 λ/

12 Using phasors to calculate diffraction patterns Phasor10.html First: Add two waves From geometry of figure, A=2A 0 cos(δ/2) same result as we obtained using trig identities last lecture. 12

13 Using phasors to add three waves A 0 sin(α) + A sin(α+δ) + A sin(α+2δ) A A 0 A 0 destructive interference when δ=120 13

14 In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. The container is surrounded by air. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is A. 1 only B. 2 only C. 3 only. 1 and 2 E. 2 and 3

15 In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. The container is surrounded by air. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is A. 1 only B. 2 only C. 3 only. 1 and 2 E. 2 and 3

16 The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes near the center of the interference pattern A. increases by a factor of 2. B. increases by a factor of 4. C. depends on the width of the slits.. decreases by a factor of 2. E. decreases by a factor of 4.

17 The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes near the center of the interference pattern A. increases by a factor of 2. B. increases by a factor of 4. C. depends on the width of the slits.. decreases by a factor of 2. E. decreases by a factor of 4.

18 Which of the phasor diagrams shows the first minimum for five equally spaced in-phase sources?

19 Which of the phasor diagrams shows the first minimum for five equally spaced in-phase sources?

20 The size of the smallest things that can be seen with an optical microscope is limited by diffraction. Which of the following could help a microscopist see smaller things? A. A more powerful microscope could be used. B. The microscope could have a lens with a shorter focal length. C. The microscope could have a lens with a longer focal length.. The diameter of the lens could be smaller. E. Light with a shorter wavelength could be used.

21 The size of the smallest things that can be seen with an optical microscope is limited by diffraction. Which of the following could help a microscopist see smaller things? A. A more powerful microscope could be used. B. The microscope could have a lens with a shorter focal length. C. The microscope could have a lens with a longer focal length.. The diameter of the lens could be smaller. E. Light with a shorter wavelength could be used.