The Wave Nature of Light - Sections 24.4 - 24.6

Announcements Review Diffraction by a Single Slit Final QuestionsQuestionA viewing screen is separated from a double slit by 4.80 m. The distance between the two slits is 0.0300 mm.Monochromatic light is directed toward the double slit and forms and interference pattern on the screen. The firstdark fringe is 4.50 cm from the center line on the screen. Determine the wavelength of the light.AnswerLet y = 4.50 cm be the distance of the first dark fringe from the center lineThen, tanθ dark = y/L, where L = 4.80 m is the distance to the viewing screenSolving for θ dark , we find thatθ dark = tan −1 ( yL) ( )= tan −1 4.50 × 10−2 m= 0.537 ◦4.80 mFurthermore, dark fringes are caused by destructive interference so(d sinθ dark = m + 1 )λ2Solving for λ (and substituting m = 0), we find thatλ = 2d sinθ dark = 2(0.0300 × 10 −3 m)sin(0.537 ◦ ) = 5.62 × 10 −7 m = 562 nmThe Wave Nature of Light