contestada

Light of wavelength 530.00 nm is incident normally on a diffraction grating, and the first‑order maximum is observed to be 33.0∘ from the normal. How many slits per millimeter are marked on the grating?

Respuesta :

lublana

Answer:

1028 slits/mm

Explanation:

We are given that

Wavelength of light, [tex]\lambda=530nm=530\times 10^{-9} m[/tex]

1nm=[tex]10^{-9} m[/tex]

[tex]\theta=33^{\circ}[/tex]

n=1

We have to find the number of slits per mm are marked on the grating.

We know that

[tex]dsin\theta=n\lambda[/tex]

Using the formula

[tex]dsin33^{\circ}=1\times 530\times 10^{-9}[/tex]

[tex]d=\frac{530\times 10^{-9}}{sin33^{\circ}}[/tex]

[tex]d=9.731\times 10^{-7} m[/tex]

1m=[tex]10^{3}mm[/tex]

[tex]d=9.731\times 10^{-7}\times 10^3[/tex]mm

[tex]d=0.0009731mm[/tex]

Number of slits=[tex]\frac{1}{d}[/tex]

Number of slits=[tex]\frac{1}{0.0009731}[/tex]/mm

Number of slits=1028/mm

Hence, 1028 slits/mm are marked on the grating.

Numenius

Answer:

1027.6 lines per mm.

Explanation:

wavelength = 530 nm

order, m= 1

Angle = 33 degree

Let the slits per mm is 1/d.

So,

[tex]m \lambda = d sin A\\\\1\times 530\times 10^{-6} = d sin 33\\\\\frac{1}{d} = 1027.6 lines per mm[/tex]