Light containing two different wavelengths passes through a diffraction grating

Question

Light containing two different wavelengths passes through a diffraction grating with 1,100 slits/cm. On a screen 15.5 cm from the grating, the third-order maximum of the shorter wavelength falls midway between the central maximum and the first side maximum for the longer wavelength. If the neighboring maxima of the longer wavelength are 8.44 mm apart on the screen, what are the wavelengths in the light? (Hint: Use the small angle approximation.)

a) ______ nm (longer wavelength)

b) _______ nm (shorter wavelength)

Explanation / Answer

d= 1/N = 1/ 1,100 slits/cm = 9.09 * 10^-6 m

he spacing between the successive maxima is

      y = L / d

The longer wavelength is

_maax= y * d / L

           =(8.44mm)(9.09*10-6 m ) /0.155

           =494.96 nm.

the third order maximum falls halfway between thecentral maximum and the first order maximum of the longerwavelength

      3 _min =(1/2) 494.96 nm

_min= (1/6)494.96 =82.49nm

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