PHYSICS - CLUTCH CH 32: WAVE OPTICS.

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2 CONCEPT: DIFFRACTION Remember! Light travels in a straight line so long as it isn t disturbed - This allows light to be described as RAYS A common way to disturb light is to have it encounter a SLIT a small opening between two barriers - The slit is the only passage for the light through the barriers - Depending on the WIDTH of the slit, the rays may OR MAY NOT be disturbed DIFFRACTION refers to the phenomenon of light rays being spread apart when encountering a slit - Diffraction will not occur for just ANY slit The slit must be SMALL compared to the wavelength L > L < L L Light passing through a slit acts differently when diffraction is ignored: No diffraction Diffraction Page 2

3 CONCEPT: DIFFRACTION WITH HUYGENS PRINCIPLE Remember! Huygens Principle dictates how new wave fronts are going to be produced: 1) An old wave front produces spherical wavelets 2) The new wave front is the tangent line across the apexes of the wavelets For DIFFRACTION, the smaller the slit, the fewer wavelets are allowed through: L > L ~ L < In reality, you can never make the slit so small that you achieve a SINGLE wavelet produced There will always be multiple wavelets produced in the slit Light will come out of two different parts of the slit at DIFFERENT angles The light will with itself θ If two slits are separated by d L you CAN consider a ray from each slit at a single angle Each light ray will with each other θ Both the single slit and the double slit produce distinct Double Slit Single Slit Page 3

4 CONCEPT: YOUNG S DOUBLE SLIT EXPERIMENT A beam of light shown onto a double slit was thought to produce a single spot of brightness - However, when this experiment is performed, this is not the case - What happens is there are multiple bright spots Expected Demonstrated - This diffraction pattern is due to Each slit produces a light ray in every direction - Some light rays constructively interfere [ DARK / BRIGHT ] FRINGES - Some light rays destructively interfere [ DARK / BRIGHT ] FRINGES The BRIGHT FRINGES are located at angles given by sin θ m = for m = 0, 1, 2, 3, The DARK FRINGES are located at angles given by d m θ m n = 0 m = 0 θ n sin θ n = for n = 0, 1, 2, 3, n EXAMPLE: A 650 nm laser is shown through a double slit of 10 mm separation. What angle is the 4 th brightest fringe located at? If the double slit is 2.8 m from the screen, how far from the brightest fringe is the 4 th brightest? Page 4

5 PRACTICE: WIDTH OF BRIGHT FRINGES A 450 nm laser shines light through a double slit of 0.2 mm separation. If a screen is placed 4 m behind the double slit, how wide are the bright fringes of the diffraction pattern? Page 5

6 EXAMPLE: UNKNOWN WAVELENGTH OF LASER THROUGH DOUBLE SLIT A laser of unknown wavelength shines monochromatic light through a double slit of 0.2 mm separation. If a screen is 5.5 m behind the double slit, you find the angular separation of each bright fringe to be 0.15 o. What is the wavelength of the laser? Page 6

7 CONCEPT: SINGLE SLIT DIFFRACTION Light shone through a double slit has unexpected results if you do not consider diffraction - Likewise, light shone through a single slit also displays a diffraction pattern The big difference between double slits and single slits is the central bright spot - In a double slit, the central bright spot is the same width as the others - In a single slit, the central bright spot is TWICE as wide as the others Like in a double slit, the diffraction pattern is due to - When light is exiting the slit, light leaves different parts of slit at different angles - Light that constructively interferes [ DARK / BRIGHT ] fringes - Light that destructively interferes [ DARK / BRIGHT ] fringes DARK FRINGES are located at angles given by m sin θ m = for m = 1, 2, 3, d θ m m = 1 EXAMPLE: A 450 nm laser is shown through a single slit of width 0.1 mm. If the screen is a distance of 140 cm away from the slit, how wide is the central bright spot? Page 7

8 PRACTICE: WIDTH OF AN UNKNOWN SINGLE SLIT Light from a 600 nm laser is shown through a single slit of unknown width. If a screen is placed 4.5 m behind the slit captures a diffraction patter with a central bright fringe of width 20 mm, what is the width of the single slit? Page 8

9 EXAMPLE: NUMBER OF DARK FRINGES ON A SCREEN Light from a 500 nm laser is shown through a single slit of width 0.5 mm, with a screen placed 3.5 m from the slit. If the screen is 2 cm wide, how many dark fringes can fit on the screen? Page 9