Answer:
[tex]\lambda=648\,\,nm[/tex]
which corresponds to red color
Explanation:
Recall that the formula for the maximum condition of interference when light of wave length [tex]\lambda[/tex] , for slit separation d, screen distance D, displacement from the center line y, and order m is given by:
[tex]y=\frac{m\,\lambda\,D}{d}[/tex]
So in our case, d = 21.6 micrometers, D = 2.5 m, y = 0.375 m, m = 5, and [tex]\lambda[/tex] is the unknown we solve for:
[tex]y=\frac{m\,\lambda\,D}{d}\\0.375\,\,m = \frac{5\,\lambda\,(2.5)}{21.6\,10^{-6}}\\\lambda=\frac{0.375\,*\,21.6\,\,10^{-6}}{5\,*\,2.5} \\\lambda=648\,\,nm[/tex]
And this wavelength corresponds to the red color (between about 625 nm and 740 nm)
