Minimum Glass Thickness (m) for Light of l=610nm, d=1.30mm, L=2.00m, n=2.2

[pooka]

A pair of slits separated by d = 1.30 mm is illuminated with light of l = 610 nm wavelength and falls on a screen L = 2.00 m away. A piece of glass with index of refraction n = 2.2 is placed at one slit. If the maxima shift is Dx/2, and falls on a minimum, what was the minimum glass thickness (in meters)?

What I did:
I first found Dx using the equation: Dx = lL/d and got an answer of 9.38*10^-4

Then because it says Dx/2. I divided that number by 2.

After that, I wasn't sure which equation to use. The only equation that seemed likely was the t = (m + 1/2)λ/(2n) but in this equation, I can't use the number (Dx/2) that I've calculated. Am I using the right equation?

 

[rl.bhat]

What I did:
I first found Dx using the equation: Dx = lL/d and got an answer of 9.38*10^-4

Then because it says Dx/2. I divided that number by 2.

Dx gives you the distance of the first maximum from the central bright fringe and ( Dx + Dx/2) gives you the distance of the first maximum from the central bright fringe after introducing the thin plate.
From Dx and Dx + Dx/2, you can find the path difference between the two rays coming from the two sources by using the expression dx = Dx*d/D
Difference in the path difference is due the the normal shift produced in the thin glass plate.
Using the expression for the normal shift you can find the minimum thickness of the plate.

 

[Moetasim]

Your approach is correct. The equation you mentioned, t = (m + 1/2)λ/(2n), is the correct equation to use for this problem. However, since you have already calculated Dx/2, you can substitute that value in for t and solve for the minimum glass thickness, t. This will give you the value in meters. Just remember to convert your wavelength (l) from nanometers to meters before substituting it into the equation.