Answer:
[tex]5.896\times 10^{-7}\ \text{m}[/tex]
Explanation:
D = Distance of the screen from the light source = 2.2 m
d = Distance between slits = 0.46 mm
m = Order
Distance between adjacent bright fringes is 2.82 m
[tex]y_{m+1}-y_m=2.82\ \text{mm}\\\Rightarrow \dfrac{D(m+1)\lambda}{d}-\dfrac{Dm\lambda}{d}=2.82\times 10^{-3}\\\Rightarrow \dfrac{D\lambda}{d}(m+1-m)=2.82\times 10^{-3}\\\Rightarrow \lambda=\dfrac{d}{D}2.82\times 10^{-3}\\\Rightarrow \lambda=\dfrac{0.46\times 10^{-3}\times 2.82\times 10^{-3}}{2.2}\\\Rightarrow \lambda=5.896\times 10^{-7}\ \text{m}[/tex]
The wavelength of the light that falls on the slits is [tex]5.896\times 10^{-7}\ \text{m}[/tex].
