Light of wavelength 710 nm passes through two narrow slits 0.66 mm apart. The screen is 2.00 m away. A second source of unknown wavelength produces its second-order fringe 1.25 mm closer to the central maximum than the 710-nm light. What is the wavelength of unknown light?

The wavelength is 503 nm  

Explanation:

Considering constructive interference , this means that route(path) difference is equal to the product of order of fringe and wavelength of the light

 i.e   dsinθ  = m

Where  is the wavelength of light  and m is the order of the fringe

    Looking at θ to be very small , sin θ can be approximated to  θ

              and  

Substituting this into the above equation

      making x the subject

      This above equation will give the value of the distance of the order fringe of the wavelength from the central fringe

       Replacing with the value given in the question we have

  = 710 nm  m = 2  d =0.66 mm , l = 2.0 m

 The separation of the second fringe from central maximum is 4,303 mm    

To obtain the separation of the second order fringe of the unknown light from central maximum

Now to obtain the wavelength of this second source

                   from

Now substituting 3,053 mm for 2.0 mm for l , 0.66 mm  for d and 2 for m in the above formula