Diffraction and interference of light

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  1. Diffraction and Interference of Light
  2. Introduction to refraction of light and interference
  3. Measuring the wavelength of light wave using Young's equation
  1. Two slits experiment is performed to measure the wavelength of red light. The silts are 0.0160 mm apart. A screen is placed 0.500m away and the separation between the central bright line and the first-order bright line is found to be 21.1mm. What is the wavelength of the red light?
    1. Yellow- orange lamp from a sodium lamp of wavelength 597 nm is aimed at two slits separated by 1.80 x 10-6 m. What is the distance from the central line to the first-order yellow line if the screen is 0.400m from the slits?
      1. A monochromatic light of wavelength of 456nm falls on a single-slit with width 0.085mm. The slit is located 65cm from the screen. How far from the center of the central band is the first dark band?
        1. Light from a He-Ne laser (λ=523.6nm\lambda = 523.6 nm) falls on a slit of unknown width. A pattern is formed on a screen 1.12m away on which the first dark band is 5.7mm from the center of the central bright band. How wide is the slit?
          Topic Notes

          In this lesson, we will learn:

          • Young’s two-slit experiment and diffraction of light
          • Interference fringes
          • Coherent waves
          • Diffraction of white light
          • Measuring the wavelength of light wave
          • Single- slit diffraction


          Young’s two-slit experiment and diffraction of light

          A directed beam of light at two closely spaced narrow slits in a barrier gets diffracted and rays from two slits overlap. A pattern of bright and and dark bands can be seen on the screen.

          Diffraction and Interference of Light

          Interference Fringes

          The bright and dark bands that can be seen on the screen as the result of light interference. The bands are the result of constructive (crests overlap) and destructive (crests meet troughs) interference of light waves form the two slits.

          Coherent Waves

          A narrow slit is placed in front of a monochromatic light (light with only one wavelength) produces coherent waves. Crests reach the same point at the same time as do the troughs.
          Diffraction of monochromatic light results in a bright central band on the screen as the result of constructive interference, other bright bands are placed on either sides. Between the bright bands dark areas are located as the result of destructive interference.

          Diffraction of white light

          When white light is used in a double-slit experiment, diffraction causes the appearance of colored spectra instead of bright and dark bands.

          Measuring the wavelength of light wave

          The wavelength of light waves using double-slit interference can be measured using:

          λ=xdL\large \lambda = \frac{xd}{L}

          x= x = distance between the central band and the first bright
          L=L = distance between the slits and the screen
          d= d = distance between two slits
          λ= \lambda = wavelength

          Single- slit diffraction
          • In single-slit diffraction the x is the distance between the central bright band and the first dark band
          • x= x = λ2\large \frac{\lambda}{2}
          • L=w2, L = \frac{w}{2}, (w is the width of the slit)
          • XL \frac{X}{L} λ/2w/2=λw⇒x=λLw\large \frac{\lambda / 2} {w / 2} = \frac{\lambda}{w} \Rightarrow x = \frac{\lambda L} {w} (distance between the central bright band the and first dark band)