Two-slit interference with two light sources?

Question

Light of wavelength 579 nm incident on a pair of slits produces an interference pattern on a distant screen in which the separation between the bright fringes is 0.53 cm. A second light source when incident on the same slits produces an interference pattern with a separation of 0.62 cm between bright fringes. What is the wavelength of the second source? [Hint: Use a small-angle approximation.]

in nm

Answer 1

The distance y between fringes is proportional to wavelength. (The small-angle equation is y = m*lambda*D/d; see the ref.)

So the 2nd source has a wavelength = 579*0.62/0.53 = 677.3 nm.

Answer 2

The equation for the separation of fringes in Young's double slit is:-

          Separation distance   =   wavelemgth * D / a

where "a"  = distance  apart of double slits

           "D"  =  distance from double slits to screen

Here,  "a" and "D", stay the same , so are constants,

       Therefore  separation  is proportional  to  wavelength

Since separation increases  by  0.62 / 0.53   =   1.170 times,

Then wavelength does the same.

New wavelength   =   579 * 1.170    =     677 nm.