Answer:
[tex]5.25\times10^{-8} m[/tex]
Explanation:
[tex]d[/tex] = separation of the slits = 0.21 mm = 0.00021 m
[tex]D[/tex] = Screen distance = 59 cm = 0.59 m
[tex]\lambda[/tex] = wavelength of the light
tex]y_{n}[/tex] = location of nth minima on the screen
[tex]y_{5}[/tex] = location of fifth minima on the screen
[tex]y_{1}[/tex] = location of first minima on the screen
location of nth minima on the screen is given as
[tex]y_{n} = \frac{(2n - 1) D \lambda}{2d}[/tex]
For n = 1
[tex]y_{1} = \frac{(2(1) - 1) D \lambda}{2d}\\y_{1} = \frac{(0.5) D \lambda}{d}[/tex]
For n = 5
[tex]y_{5} = \frac{(2(5) - 1) D \lambda}{2d}\\y_{1} = \frac{(4.5) D \lambda}{d}[/tex]
Given that:
[tex]y_{5} - y_{1} = 0.00059\\\frac{(4.5) D \lambda}{d} - \frac{(0.5) D \lambda}{d} = 0.00059\\\frac{(4) D \lambda}{d} = 0.00059\\\frac{(4) (0.59) \lambda}{0.00021} = 0.00059\\ \lambda = 5.25\times10^{-8} m[/tex]