Question

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?

Answer 1

649.8420 nm

Step-by-step explanation:

We have given
`\Theta _1=24^(\circ) \ and\ \Theta _2=39^(\circ)`

`\lambda _1=420\ nm` we have to find unknown wavelength that is
`\lambda _2`

The condition for constructive interference is
`dsin\Theta =n\lambda`

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

Using constructive interference equation

`dsin\Theta _1=n\lambda _1` ---------eqn 1

`dsin\Theta _2=n\lambda _2`---------eqn 2

On dividing eqn 1 by eqn 2

`(\lambda _1)/(\lambda _2)=(sin\Theta _1)/(sin\Theta _2)`

`(420)/(\lambda _2)=(sin24^(\circ))/(sin39^(\circ))`

`\lambda _2=649.8420\ nm`