For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 24°. for an unknown wavelength, the same grating produces a bright fringe at an angle of 39°. in both cases the bright fringes are of the same order m. what is the unknown wavelength?

649.8420 nm

Explanation:

We have given

we have to find unknown wavelength that is

The condition for constructive interference is

Where d is distance between slits is angle of emergence and n is order of maxima

Using constructive interference equation

---------eqn 1

---------eqn 2

On dividing eqn 1 by eqn 2

distance = 150m

displ = root (50 ^2 + 100^2)

root(2500+10000)

root 125000