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Double Slit Interference

Double Slit Interference. Tips…. Words like “maximum” and “bright” refer to regions of constructive interference. Similarly, “ minumum ” and “dark” refer to destructive interference. Conditions…. Constructive: dsin q = dy /L = m l Destructive: dsin q = dy /L = (m + ½ ) l.

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Double Slit Interference

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  1. Double Slit Interference

  2. Tips… • Words like “maximum” and “bright” refer to regions of constructive interference. • Similarly, “minumum” and “dark” refer to destructive interference.

  3. Conditions… • Constructive: dsinq = dy/L = ml • Destructive: dsinq = dy/L = (m + ½ )l

  4. Using the equations… • d is the distance between the slits. Very small. Usually x10-5 meters • y is the distance to the bright or dark spot on the screen. Measured from the reference line to the spot. Usually centimeters • L is the distance to the screen. Usually meters • l is the wavelength. Usually in nanometers. • m is the “order” which bright or dark spot you are measure to (1st, 2nd, …)

  5. Using the equations • You must be consistent with your units! Put everything in meters or centimeters, or millimeters. Whatever – but consistent.

  6. m and y • “m” and “y” are related. • If the question says: “The third bright spot is 6cm from the reference line…” • Then use m=3 and y=6cm with the constructive interference equation • But they usually aren’t worded that obviously…

  7. Usual wording… • Since it is virtually impossible to know where the reference line is, the questions won’t explicitly tell you the y value. • More common: “The distance between the first and fifth bright spots is 12cm.” • To solve: find the distance between consecutive bright spots and use that distance as your y with m=1.

  8. Best way… • Since the bright and dark spots are uniformly distributed, always try to figure out the distance between consecutive bright OR consecutive dark spots. • Then use that distance as the y with m=1 and condition for constructive interference.

  9. Example #1 • Red light (l = 650nm) passes through a double slit and hits a screen 3.0m away. The distance between dark spots is 1.5cm. What is the distance between the slits? • What are y and m? • Solve…

  10. Example 2 • Orange light (l = 600nm) illuminates a double slit. The slit separation is 0.025mm. On the screen, the distance between 4 dark spots is 8.0cm. How far away is the screen? • Sketch 4 dark spots • Figure out the spacing between consecutive bright or dark. • Use that as y with m=1 constructive

  11. Example 3 • Ultraviolet light (l = 340nm) shines on a double slit. The screen is 2.0m away. The distance between the 1st and 6th dark spots is 15cm. What is the slit separation?

  12. Example 4 • Light with l = 450nm illuminates slits that are 6mm apart. The screen is 1.5m away. Find the distance from the reference line to the third-order minimum.

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