Answer: 655.7 nm
Explanation:
Given
The slits are separated by [tex]d=0.510\ mm[/tex]
Distance between slits and screen is [tex]D=2.24\ m[/tex]
Adjacent bright fringes are [tex]\beta =2.88\ mm[/tex] apart
Also, the distance between bright fringes is given by
[tex]\Rightarrow \beta =\dfrac{\lambda D}{d}\quad [\lambda=\text{Wavelength of light}]\\\\\text{Insert the values}\\\\\Rightarrow 2.88\times 10^{-3}=\dfrac{\lambda \cdot 2.24}{0.510\times 10^{-3}}\\\\\Rightarrow \lambda =\dfrac{2.88\times 10^{-3}\times 0.510\times 10^{-3}}{2.24}\\\\\Rightarrow \lambda =0.6557\times 10^{-6}\ m\\\Rightarrow \lambda =655.7\ nm[/tex]
