Question

a monochromatic beam of light of wavelength 546 NM falls on the grating normally and gives a second-order image at an angle of 45 degree the grating element is of the order of​

Answer 1

Answer: where d is distance between slits of grating, θ is angle of diffraction,

n is order of diffraction and λ is wavelngth of incident light .

d = 1/ N , where N is number of lines per unit length

we have , d = 1/N = 1/4250 cm   or  d = (1/4250)×10-2 m

Hence we get diffraction angle from eqn.(1),

(1/4250) × 10-2 sinθ = 5900  × 10-10

we get angle θ = 14.52°

Explanation:

Answer 2

Answer:

The grating element is of the order of 1.544×10⁻⁶m.

Explanation:

For the transmission grating,

$dsin\theta=n\lambda$            (1)

Where,

d=distance between the slits of grating

θ=is the angle of diffraction

n=order of diffraction

λ=wavelength of incident light

From the question we have;

θ=45°

n=2

λ=546nm=546×10⁻⁹m

By putting these values in equation (1) we get;

$dsin45\textdegree=2\times 546\times 10^-^9$

$d\frac{1}{\sqrt{2}}=1092\times 10^-^9$

$d=1544\times 10^-^9$

$d=1.544\times 10^-^6m$

Hence, the grating element is of the order of 1.544×10⁻⁶m.