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Light from a laser strikes a diffraction grating that has 5 314 grooves per centimeter. The central and first-order principal maxima are separated by 0.488 m on a wall 1.78 m from the grating. Determine the wavelength of the laser light. (In this problem, assume that the light is incident normally on the gratings.)

Respuesta :

Answer:

wavelength = 497.03 × [tex]10^{-9}[/tex] m

Explanation:

given data

diffraction grating = 5 314

separated = 0.488 m

distance = 1.78 m

to find out

wavelength of the laser light

solution

we first find here angle of the first maximum with the center that is

a = [tex]tan^{-1} \frac{0.488}{1.78}[/tex]

a = 15.33°

and

grating distance will be = [tex]\frac{1}{5314}[/tex]

grating distance g = 1.88 × [tex]10^{-6}[/tex] m

so now equation for the wavelength will be

wavelength = g × [tex]\frac{sin(a)}{n}[/tex]

here n = 1

wavelength = g × [tex]\frac{sin(a)}{n}[/tex]

wavelength = 1.88 × [tex]10^{-6}[/tex] × [tex]\frac{sin(15.33)}{1}[/tex]

wavelength = 497.03 × [tex]10^{-9}[/tex] m

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