Question

With light from a gaseous discharge tube incident normally on a grating with slit separation 1.73 µm, sharp maxima of green light are produced at angles = +-17.6°, 37.3°, -37.1°, 65.2°, and -65.0°. Compute the wavelength of the green light that best fits these data.

Answer 1

for diffraction through diffraction grating,

d*sin(theta)=m*lambda

where d=slit width

theta=angle of diffraction

m=order of diffraction

lambda=wavelength of the light

given that d=1.73 um

for theta=17.6 degrees

let m=1

==>1.73*10^(-6)*sin(17.6)=1*lambda

==>lambda=523.1 nm

now, calculate the values for lambda for other cases and if we can show that value of m for all other angles are integers, then this is the correct value of wavelength.

theta=-17.6 degrees==>m=-1

theta=37.3 degrees ==> m=2.0041 =2 (approx)

theta=-37.1 degrees ==>m=-1.9949 =-2 (approx)

theta=65.2 degrees ==> m=3.0022=3 (approx)

theta=-65.1 degrees ==> m=-2.9973=-3 (approx)

so as we can see, all the values are very very close to integer values.

hence wavelength of the light incident is 523.1 nm