Question

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.)

Answer 1

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