Answer:
[tex]1.199\ \mu\text{m}[/tex]
Explanation:
[tex]\lambda[/tex] = Wavelength = 600 nm
D = Distance of the light source from screen = 3 m
y = Distance of first order bright fringe from center = 4.84 mm
d = Distance between slits
m = Order = 1
We have the relation
[tex]y=\dfrac{D\lambda}{d}\\\Rightarrow d=\dfrac{D\lambda}{y}\\\Rightarrow d=\dfrac{3\times 600\times 10^{-9}}{4.84\times 10^{-3}}\\\Rightarrow d=0.0003719\ \text{m}[/tex]
From the question we have
[tex]y=\dfrac{\dfrac{1}{2}3\lambda}{d}\\\Rightarrow \lambda=\dfrac{2}{3}yd\\\Rightarrow \lambda=\dfrac{2}{3}\times 4.84\times 10^{-3}\times 0.0003719\\\Rightarrow \lambda=0.000001199\ \text{m}=1.199\ \mu\text{m}[/tex]
The required wavelength of light is [tex]1.199\ \mu\text{m}[/tex].
