In optics, a diffraction grating is an optical component with a periodic structu

Question

In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beans travelling in different directions. The directions of these beams depend on the spacing of the grating and the wave length of the light so that the grating acts as the dispersive element. This "super prism" aspect of the diffraction grating leads to application for measuring atomic spectra in both laboratory instruments and telescopes. A large number of parallel, closely spaced slits constitutes a diffraction grating. The condition for maximum intensity is the same as that for the double slit or multiple slits, but with a large number of slits the intensity maximum is very sharp and narrow, providing the high resolution for spectroscopic applications. Thus, when light is normally incident on the grating, the diffracted light will have maxima at angles given by: d sin theta_m = m lambda Where d is the grating spacing and d = 1/C, & C is the grating constant = 600 lines/mm m is the order m = 1 theta is the angle and lambda is the wavelength Distance from grating to central maximum in the screen X = cm Grating Spacing d = 1/C = 1/6000 cm = 1/600000 m Procedure: Inspect the following diagram of an experiment. A white light from Hydrogen gas is incident on a grating with grating constant C = 600 lines/mm. The diffracted maximum are shown on the screen. Step 1. Measure the distance from the grating to the center maximum on the screen and record it on the top of the data table. Step 2. Measure the distance from the center maximum to the individual maximum and record it on the data table. This is your Y. Step 3. Find the individual angle by using formula Theta = tan^-1 (Y/X) for each spectral lines and record it on the data table. Step 4. Repeat step 2 and step 3 until you finish.

Explanation / Answer

For a multislit diffraction grating
the maximas are given at angle theta-n with respect to the horizontal with the following formula
d*sin(theta-n) = n*Lambda
where lambda is the wavelength of the light used
d is the grating slit seperation
now, d = 1/C [ where C is num,bner of lines per m ina difraction grating]
so, d = 1/C = 1/6000 cm = 1/6000,00 m

now from the graph, distance from the screen, D = 10 cm = 0.1 m

Color    Y in cm theta       Wavelength In m   Avg
Red   L 4.3      0.406098058 6.5838E-07        6.5838E-07
      R 4.3      0.406098058 6.5838E-07
      L 3        0.291456794 4.78913E-07       4.78913E-07
      R 2.98     0.289620924 4.75982E-07
      L 2.7      0.263711834 4.34443E-07       4.34443E-07
      R 2.7      0.263711834 4.34443E-07
      L 2.4      0.235544981 3.88955E-07       3.88955E-07
      R 2.34     0.229864084 3.79742E-07

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