Respuesta :
Answer: [tex]7.35\°[/tex]
Explanation:
The diffraction angles [tex]\theta_{n}[/tex] when we have a slit divided into [tex]n[/tex] parts are obtained by the following equation:
[tex]dsin\theta_{n}=n\lambda[/tex] (1)
Where:
[tex]d[/tex] is the width of the slit
[tex]\lambda[/tex] is the wavelength of the light
[tex]n[/tex] is an integer different from zero
Now, the first-order diffraction angle is given when [tex]n=1[/tex], hence equation (1) becomes:
[tex]\theta_{1}=arcsin(\frac{\lambda}{d})[/tex] (2)
We are told the diffraction grating has 2000lines per cm, this means:
[tex]d=\frac{1cm}{2000}=0.0005cm=0.000005m[/tex]
In addition we know [tex]\lambda=640nm=640(10)^{-9}m[/tex]
Solving (2) with the known values we will find [tex]\theta[/tex]:
[tex]\theta_{1}=arcsin(\frac640(10)^{-9} m}{0.000005m})[/tex] (3)
[tex]\theta_{1}=7.35\°[/tex] (4) This is the angle at which red light appears in first-order spectrum.
Explanation:
It is given that,
If the grating has 2000 lines per centimeter.
Wavelength, [tex]\lambda=640\ nm=640\times 10^{-9}\ m[/tex]
The principal maxima is given by :
[tex]d\ sin\theta=n\lambda[/tex]
Since, d = 1/N and n = 1
So, [tex]d=\dfrac{1}{2000\ lines/cm}=0.0005\ cm[/tex]
[tex]d=5\times 10^{-6}\ m[/tex]
[tex]sin\theta=\dfrac{\lambda}{d}[/tex]
[tex]sin\theta=\dfrac{640\times 10^{-9}}{5\times 10^{-6}}[/tex]
[tex]\theta=7.35^{\circ}[/tex]
So, the angle is 7.35 degrees. Hence, this is the required solution.
