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

Answer:

649.8420 nm

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

$\frac{\lambda _1}{\lambda _2}=\frac{sin\Theta _1}{sin\Theta _2}$

$\frac{420}{\lambda _2}=\frac{sin24^{\circ}}{sin39^{\circ}}$

$\lambda _2=649.8420\ nm$