Answer:
550 nm
Explanation:
The formula for the double-slit diffraction experiment is:
[tex]y=\frac{m\lambda D}{d}[/tex]
where
y is the distance of the m-th maximum from the central fringe
[tex]\lambda[/tex] is the wavelength of the light used
D is the distance of the screen from the slits
d is the separation between the slits
In this problem we have:
[tex]d=0.3 mm = 0.3\cdot 10^{-3} m[/tex] is the distance between the slits
[tex]D=1.5 m[/tex] is the distance of the screen
We also know that the distance between the 3rd and 5th order maximum is 5.5 mm, which means that:
[tex]y_5-y_3 = 5.5 mm = 5.5\cdot 10^{-3} m[/tex]
And we can rewrite this as:
[tex]y_5-y_3 = \frac{5\lambda D}{d}-\frac{3\lambda D}{d}=\frac{2\lambda D}{d}[/tex]
where we used respectively m=3 and m=5. If we know solve for [tex]\lambda[/tex], we find the wavelength:
[tex]\lambda = \frac{(y_5-y_3) d}{2 D}=\frac{(5.5\cdot 10^{-3})(0.3\cdot 10^{-3})}{2(1.5)}=5.5 \cdot 10^{-7} m=550 nm[/tex]
