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1 P1X: Optics, Waves and Lasers Lectures, 2005-06. Lecture 4: Interference and diffraction of light (I) Youngs two slit experiment (Y&F 35.2) o To observe.

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Presentation on theme: "1 P1X: Optics, Waves and Lasers Lectures, 2005-06. Lecture 4: Interference and diffraction of light (I) Youngs two slit experiment (Y&F 35.2) o To observe."— Presentation transcript:

1 1 P1X: Optics, Waves and Lasers Lectures, Lecture 4: Interference and diffraction of light (I) Youngs two slit experiment (Y&F 35.2) o To observe interference of light one needs to set-up two independent, coherent, monochromatic (same frequency) light sources. o Coherent light sources are difficult to make since light is emitted by the random agitation of atoms (we will see later on that lasers can be sources of coherent light). o To achieve two coherent sources of light, we can use a common source and split it such that the light emerges from two secondary sources, so the relative phase between them is always the same. S0S0 S1S1 S2S2

2 2 P1X: Optics, Waves and Lasers Lectures, Youngs two slit experiment (Cont.) o Young (1800) set up an experiment to demonstrate the wave nature of light. o A monochromatic beam of light is incident on a single slit S 0. This acts as a source of wavefronts onto two slits S 1 and S 2. o The coherent waves interfere with each other forming a pattern of light and dark bands on a screen some distance from the two slits.

3 3 P1X: Optics, Waves and Lasers Lectures, Geometry of Youngs two slit experiment The triangle S 1 S 2 Q means that: S 1 Q = d sin If the screen is at a distance R which is much larger than the separation d of the two slits (R could be a few metres and d a few millimetres) then r 1 and r 2 are nearly parallel to each other and is small: y r1r1 S1S1 S2S2 R r2r2 Intensity d d sin = r 2 - r 1 Q P

4 4 P1X: Optics, Waves and Lasers Lectures, o Constructive interference: bright fringes oDestructive interference: dark fringes

5 5 P1X: Optics, Waves and Lasers Lectures, o Example 35-1 (Y&F): In a two slit interference experiment, the slits are 0.20 mm apart, and the screen at a distance of 1.0 m. The third bright fringe (not counting the central bright fringe) is displaced by 7.5 mm. Find the wavelength of light used. Third fringe: m=3, R=1.0 m, d=0.2 mm, R>>d Another possibility: m= -3 y m = -7.5 mm

6 6 P1X: Optics, Waves and Lasers Lectures, o Example L61 (Example book): Light from a source containing 2 wavelengths of 567 nm and 486 nm illuminates a double slit arrangement with d=1.0 mm and R=1.50 m. At what distance from the central fringe on the screen will a bright fringe from one interference pattern coincide with the bright fringe from the other interference pattern. Bright fringes:

7 7 P1X: Optics, Waves and Lasers Lectures, o The waves associated with light are called electromagnetic waves. Unlike the other waves we have encountered, they dont need a medium to propagate. They can propagate in vacuum. o In the two slit experiment we have an electric field coming from S 1 : and another coming from S 2 : (frequency and amplitude are the same since the two sources are coherent). Principle of superposition: P.1463 Y&F Since: Trigonometric functions Intensity in interference patterns (Y&F, 35.3)

8 8 P1X: Optics, Waves and Lasers Lectures, o Since: Then: o Phase difference between two waves: r 2 -r 1 is called the path difference. o New wave:

9 9 P1X: Optics, Waves and Lasers Lectures, New wave has angular frequency and wave number k but the new amplitude is: with: EPEP -2E 2E

10 10 P1X: Optics, Waves and Lasers Lectures, o Intensity of light is the average power per unit area (energy per unit area per unit time): The intensity of light is proportional to the square of the amplitude of the electric field: I 0 I0I0

11 11 P1X: Optics, Waves and Lasers Lectures, o Lloyds mirror is just like Youngs two slit experiment but with only one source of light and a mirror used to create a second virtual source of light. Lloyds mirror o The source interferes with its own image in the mirror. a y r 2 S1S1 R r I d MIRROR r1r1 r2r2 S2S2 y

12 12 P1X: Optics, Waves and Lasers Lectures, There is a phase change of radians due to the reflection of the mirror (equivalent to a path difference of ). o The constructive and destructive conditions are reversed with respect to Youngs experiment and there is a dark fringe next to the mirror. Constructive interference: bright fringes Destructive interference: dark fringes EPEP BEFORE MIRROR EPEP AFTER MIRROR


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