To solve the problem we will apply the concepts related to the two slit experiment which describes the slit separation by the angle of projection as a function of the order of the bright fringe by the wavelength, this can be mathematically described as,
[tex]dsin\theta = m\lambda[/tex]
Here,
d = Slit separation
[tex]\lambda[/tex] = Wavelength
m = Order of bright fringe
At the same time the distance of the central spot is defined as,
[tex]y = \frac{m \lambda R}{d}[/tex]
Here,
[tex]\lambda[/tex]= Wavelength
R = Distance from slit to screen
Using the latest equation and rearranging to find the wavelength, we have,
[tex]\lambda = \frac{yd}{mR}[/tex]
[tex]\lambda = \frac{0.1*3^{-5}}{7*2}[/tex]
[tex]\lambda = 214.2nm[/tex]
Therefore the wavelenght of the light is 214.2nm
