Physics 3 – Dec 7, 2017 P3 Challenge – The equation of motion for the oscillation of a mass on a spring is given by y=(3.2 cm) cos (0.45 t) when a 0.100 kg mass is used. What is the spring constant of the spring in N/m? Today’s Objective – Single and Double slits

Objectives/Agenda/Assignment 9.3 Double Slit Agenda: Double Slits Multiple slits Thin films Assignment: p374 #17-26

The double slit experiment https://www.youtube.com/watch?v=Iuv6hY6zsd0 A modern take on Young’s original double slit experiment with sunlight. Creates an interference pattern with bright and dark fringes.

Double slit interference pattern creation Same assumptions as single slit diffraction. (see image) The distance between the central bright spot and the next bright spot is called the fringe spacing, y. For IB, fringe spacing is given by s and calculated as 𝑠= 𝜆𝐷 𝑑 where D is the distance to the screen and d is the distance between the slits b

Comparing one and two slits You’ll notice that a real double slit display shows characteristics of both diffraction based on slit width and the interference based on the distance between slits. (shown on the right.) The same equation applies to both, but calculates different things. One slit is a minimum condition. Two slits is a maximum condition.

Problems Red light with a wavelength of 752 nm passes through a pair of vertical slits with a separation of 6.20 x 10-5 m creating an interference pattern on a screen 0.750 m away. (Watch units) What is the distance between the central maximum and the third bright fringe to the side? What is the distance to the first dark fringe?

Single and Double Slit Review

Multiple slits Intensity of peaks increases by (N/2)2 N = the number of slits Peaks of interference become sharper N-2 number of secondary maxima appear between the primary maxima

Multiple slits Secondary maxima, get relatively smaller and smaller until they become negligible. Diffraction gratings with large N create a sharp image of primary maxima Notice we still see the diffraction envelope created by the slit width.

Thin Films When light reflects off a substance with a higher index of refraction there is a 180° phase shift This phase shift combines with the conditions of constructive and destructive interference to switch the results. Ordinarily: Constructive: path diff = (m) λ Destructive: path diff = (m+1/2) λ

Thin Films For thin films, the path difference is 2d and the wavelength of the light within the film is λ/n. Therefore: With the phase change: Constructive: 2dn = (m+1/2) λ Destructive: 2dn = (m) λ With no or two phase changes Constructive: 2dn =(m) λ Destructive: 2dn = (m+1/2) λ n is the index of refraction, m is an integer and λ is the incident wavelength, d is the thickness of the film.

Exit slip and homework Exit Slip – What is the condition for constructive interference from a thin film of n=1.25 on the surface of glass with n=1.33 if it had a thickness of d? What’s due? (homework check next class) 9.3 p374 #17-26 What’s next? (What to read to prepare for the next class) Study for Final with more Mastery Quizzes