Determining Mica Thickness Using Interference Fringes

[inflames829]

Homework Statement

A thin flake of mica (n= 1.58) is used to cover one slit of a double slit interference arrangement. The central point on the viewing screen is now covered by what had been the 9th bright fringe before the mica was used. What is the thickness of mica if light of wavelength 556nm is used? answer in microns

Homework Equations

The Attempt at a Solution

n lambda = xb/L
where
λ is the wavelength of the light,
b is the separation of the slits, the distance between A and B in the diagram to the right
n is the order of maximum observed (central maximum is n=1),
x is the distance between the bands of light and the central maximum (also called fringe distance), and
L is the distance from the slits to the screen centerpoint.


This is the only equation i can find so i assume you use it. Is this correct? and if so can someone give me hints on what values to put in for L and x. please. THANKYOU

 

[Kurdt]

The path difference when one slit is covered with mica will be slightly different.

$$\frac{xb}{L} = (n-1)t$$

where t is the thickness of the mica.

 

[Moetasim]

Yes, the equation you have provided is correct for determining the thickness of the mica using interference fringes. To solve for the thickness, we need to rearrange the equation to solve for x:

x = nλL/b

In this case, we know the values for n (9), λ (556 nm), and n (1). We also know that the distance between the slits (b) is equal to the thickness of the mica. We can measure the distance between the central maximum and the 9th bright fringe (x) using a ruler or measuring tape on the viewing screen.

To solve for L, we can use a similar method. We know the distance between the slits (b) and the distance between the slits and the viewing screen (L). We can measure the distance between the slits and the central maximum (x) using the same method as before.

Once we have all the necessary values, we can plug them into the equation and solve for the thickness of the mica in microns. Remember to convert all units to the same unit before plugging them into the equation.