Question

Light of two different wavelengths is used in a double-slit experiment. The location of the third order bright fringe for yellow-orange light (l= 541.08 nm) coincides with the location of the fourth order fringe for the other color's light. What is the wavelength, in nm, of the other light?

Answer 1

Let's name some variables:

n1: order of yellow-orange light; n1 = 3

λ1: wavelength of yellow-orange light; λ1 = 541.08 nm

n2: order of unknown light; n2 = 4

λ2: wavelength of unknown light; we will solve for this

Given these known and unknown variables, we can use the following equation to solve for λ2:

n1*λ1 = n2*λ2

Now all we have to do is plug in the variables we know and solve for λ2.

3*541.08 = 4*λ2

λ2 = 3*541.08/4

λ2 = 405.81 nm