lecture30 - Youngs double slit interference

lecture30 - Youngs double slit interference - What you...

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Unformatted text preview: What you will be able to do a/er today … Explain … Calculate … •  the refrac:ve index •  how the speed of light and wavelength change inside a medium •  the new wavelength of a light wave traveling in a with a certain refrac:ve index medium •  the path difference for light interference in a 2 ­slit experiment •  the posi:on of interference fringes •  what are dark and bright ‘fringes’ Apply … •  ra:onale for what proper:es of light change inside a medium •  interference of sound waves to light waves. The midterm ques:ons were … •  •  •  •  (a) exactly what I expected (b) somewhat like what I expected (c) somewhat different than what I expected (d) very different from what I expected I thought the exam was .. •  •  •  •  •  (a) too easy (b) easy (c) fair (d) challenging (difficult) (e) too difficult Speed of Light and Refractive Index •  c0 = 3.0 x 108 m/s (in vacuum, air) •  Inside glass: different medium so different speed (light interacts with the electrons). •  The refractive index is defined as: c !f n= = v !n f •  frequency does NOT change inside a medium Worksheet: Wed You have an instrument that gives you limited informa:on about light waves travelling through 4 different materials. It gives you a snapshot in :me and tells you Δd, the distance between two points along the wave in the medium. It also gives you Δt, the :me it takes for the A ­B wave segment to pass by (or fly by) a sta:onary observer. You want to chose a material through which the light will travel the fastest. Rank the materials, and find the n ­value of each medium B B x Medium 1 A Medium 2 A A Δd = 120 nm B A x Medium 3 x B x Medium 4 Worksheet: Today You have the same instrument that gives you a snapshot in :me and tells you Δd, the distance between two points along the wave in the medium. It also gives you Δt, the :me it takes for the A ­B wave segment to pass by (or fly by) a sta:onary observer. What is the index of refrac:on of this medium. (A) nmedium=1.00 (B) nmedium=1.40 (C) nmedium=1.90 (D) nmedium=2.40 (E) nmedium=2.90 Δd = 1.75μm B A Δt = 1x10 ­15s x From the drawing we know the length of 1.75 wavelengths = 1.75μm. So the wavelength inside the medium is: λ =1.0μm It takes 1x10 ­15 sec for 1/8 of a cycle to pass by (one cycle =T) . So 0.125 T = 1x10 ­15 sec and 1 f = = 1.25x1014 Hz T c Speed of the wave is = λ f = 1 .25x108 m /s ; nmedium =2.4 n (A) nmedium=1.00 (B) nmedium=1.40 (C) nmedium=1.90 (D) nmedium=2.40 (E) nmedium=2.90 Δd = 1.75μm B A Δt = 1x10 ­15s x Ques:on Two laser beams are turned on simultaneously at t=0. Laser beam 1 goes thru two separate 1cm thick pieces of glass, Laser beam 2 goes thru a single 2cm thick piece of glass CASE 1: glass 1 has an index of refrac:on nblue=1.5. glass 2 has an index of refrac:on ngreen=1.5 . →Do they arrive at the doGed line at the same Hme? 1cm 1cm nblue=1.5 Laser beam 1 (A) yes, same :me (B) Beam 1 arrives faster Laser beam 2 (C) Beam 2 arrives faster 2cm ngreen=1.5 14cm Ques:on Two laser beams are turned on simultaneously at t=0. Laser beam 1 goes thru two separate 1cm thick pieces of glass, Laser beam 2 goes thru a single 2cm thick piece of glass CASE 2: glass 1 has an index of refrac:on nblue=1.25. glass 2 has an index of refrac:on ngreen=1.5 . →Do they arrive at the doGed line at the same Hme? 1cm 1cm nblue=1.25 Laser beam 1 (A) yes, same :me (B) Beam 1 arrives faster Laser beam 2 (C) Beam 2 arrives faster 2cm ngreen=1.5 14cm worksheet Two laser beams are turned on simultaneously at t=0. Laser beam 1 goes thru two separate 1cm thick pieces of glass, each with an index of refrac:on nblue=1.25. Laser beam 2 goes thru a single 2cm thick piece of glass with an index of refrac:on ngreen=1.5 . →What Hme does each arrive at the doGed line ? (A) yes, same :me 1cm 1cm nblue=1.5 Laser beam 1 (B) Beam 1 arrives 17 x 10 ­12 s before beam 2 (C) Beam 1 arrives 17 x 10 ­12 s a/er beam 2 Laser beam 2 (D) Beam 1 arrives 8.5 x 10 ­12 s before beam 2 (E) Beam 1 arrives 8.5 x 10 ­12 s a/er beam 2 2cm ngreen=1.5 14cm Light as a Wave •  Young s two source interference experiment proved that light is a wave. video •  Light usually moves along straight lines but it spreads out when passing through a narrow slit or a small hole ( diffraction ). •  Light has other wave effects: interference, refraction, Doppler effect, shock waves, etc. •  Light also has particle properties, like momentum (recoil of atoms, radiation pressure) 11 Young s Double-Slit Experiment Constructive Destructive Beam illuminates both slits. Light spreads out behind each slit in the horizontal plane. Slits: Create two coherent (in phase) waves Interference leads to fringes’: dark and bright zones that can be observed on a screen – similar to change in noise intensity 1 Just like two speakers!2 Conditions for Constructive and Destructive Interference Constructive Interference path difference (in meters) phase difference (in radians) !x = m! !! = m ! 2" Destructive Interference 1 !x = (m + )! 2 1 !! = (m + ) ! 2" 2 !x !! = 2" + !!0 # worksheet A laser beam (l = 500 nm) is incident on a gra:ng with two slits separated by a distance, d, of 1.0 mm with a screen placed a distance, L, 1.0 m away. The 2 slits are so small that the light waves coming out of them can be assumed to be point sources. Since d<<L, we can assume both rays (r1 and r2) to be parallel at an angle θ. (a) are the two sources in phase? EXPLAIN in a sentence (b) Is there a path length difference? EXPLAIN in a sentence What is this arrow indicating ? (c) Try to write an equa:on for determining the height posi:on (y) of each construc:ve maxima (bright ‘fringe’). Coherence •  For interference, the point sources must be coherent. •  What is coherence ? •  Two waves are said to be coherent if they have a constant relative phase. •  Coherence in Young s experiment: The two slits are illuminated with the same source (laser). •  Normal light sources emit many waves of different frequencies at random times: incoherent. 15 Young s Double Slit Experiment •  Interference pattern: waves in phase (constructive, bright) or out of phase (destructive, dark). •  Phase difference due to path length difference Length (slit1 - screen) ≠ Length(slit2 - screen). •  Constructive: path difference ΔL= m·λ (m = 0,1,2,3...). •  Destructive: path difference ΔL = m·λ/2 •  Angle of red and blue ray almost the same, if d << L θ θ ΔL = d sin θ L 16 Young s Double-Slit Experiment •  Constructive (bright fringe) if d sin θ = mλ •  Destructive (dark fringe) if 1 ȹ ȹ d sin θ = ȹ m + ȹλ 2 Ⱥ ȹ •  Two bright fringes separated by Δm =1 (HeNe laser, typical distances): Δy = L tan( Δθ ) ≈ L sin( Δθ ) = L λ d = 2.0m θ θ ΔL L 632.8 nm = 1.3 mm 1.0 mm 4 3 2 1 0 1 2 3 4 17 ...
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