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A grating that has 3900 slits per cm produces a third- order fringe at a 28.0° angle. What wavelength of light is being used? Express your answer to two significant figures and include the appropriate units.

Respuesta :

aachen

Explanation:

Given that,

Number of slits per cm, [tex]N=3900\ lines/cm=390000\lines/m[/tex]

The third fringe is obtained at an angle of, [tex]\theta=28[/tex]

We need to find the wavelength of light used. The grating equation is given by :

[tex]d\ sin\theta=n\lambda[/tex]

[tex]d=\dfrac{1}{N}=\dfrac{1}{390000}[/tex]

[tex]d=2.56\times 10^{-6}\ m[/tex]

[tex]\lambda=\dfrac{d\ sin\theta}{n}[/tex], n = 3

[tex]\lambda=\dfrac{2.56\times 10^{-6}\times \ sin(28)}{3}[/tex]

[tex]\lambda=4.006\times 10^{-7}\ m[/tex]

[tex]\lambda=400\ nm[/tex]

So, the wavelength of the light is 400 nm. Hence, this is the required solution.

temdan2001

With the use of formula, the wavelength of light is being used is 4.0 x [tex]10^{-7}[/tex] m or 400nm

DIFFRACTION GRATING

Diffraction grating works exactly the same way as a double slit. Instead of two slits, it has thousands of slit much more of shorter fringes.

Given that a grating has 3900 slits per cm produces a third- order fringe at a 28.0° angle. The wavelength of light being used can be expressed as

sin Ф = nλ / a

Make λ the subject of the formula

nλ = a sin Φ

λ = a sin Φ / n

Where

  • λ = wavelength
  • n = 3
  • Φ = 28 degrees
  • a = 0.01 / 3900

a = 2.56 x [tex]10^{-6}[/tex] m

Substitute all the parameters into the formula

λ = (2.56 x [tex]10^{-6}[/tex] x sin 28) / 3

λ = 1.2 x [tex]10^{-6}[/tex] /3

λ = 4.0 x [tex]10^{-7}[/tex] m

λ = 400 nm

Therefore, the wavelength of light is being used is 4.0 x [tex]10^{-7}[/tex] m or 400nm

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