Answer: [tex]1.8\°[/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=3.4(10)^{-5}m[/tex] is the width of the slit
[tex]\lambda=540 nm=540(10)^{-9}m[/tex] is the wavelength of the light
[tex]n[/tex] is an integer different from zero.
Now, the second-order diffraction angle is given when [tex]n=2[/tex], hence equation (1) becomes:
[tex]dsin\theta_{2}=2\lambda[/tex] (2)
Now we have to find the value of [tex]\theta_{2}[/tex]:
[tex]sin\theta_{2}=\frac{2\lambda}{d}[/tex] (3)
Then:
[tex]\theta_{2}=arcsin(\frac{2\lambda}{d})[/tex] (4)
[tex]\theta_{2}=arcsin(\frac{2(540(10)^{-9}m)}{3.4(10)^{-5}m})[/tex] (5)
Finally:
[tex]\theta_{2}=1.8\°[/tex] (6)
