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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.)

1 Answer

4 votes

Answer:

wavelength = 497.03 ×
10^(-9) m

Step-by-step 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 =
tan^(-1) (0.488)/(1.78)

a = 15.33°

and

grating distance will be =
(1)/(5314)

grating distance g = 1.88 ×
10^(-6) m

so now equation for the wavelength will be

wavelength = g ×
(sin(a))/(n)

here n = 1

wavelength = g ×
(sin(a))/(n)

wavelength = 1.88 ×
10^(-6) ×
(sin(15.33))/(1)

wavelength = 497.03 ×
10^(-9) m

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