Question

Light with a wavelength of 576 3. ×10−9 m passes through two slits and forms an interference pattern on a screen 8.85 m away. if the linear distance on the screen from the central fringe to the first bright fringe above it is 5.36 cm, what is the separation of the slits?

Answer 1

The correct formula for the double-slit experiment is given by

`y= (n \lambda D)/(d)`
where
y is the distance of the n-th maximum from the central fringe on the screen
n is the order of the maximum
D is the distance between the slits and the screen
d is the distance between the two slits

In our problem, we are given:

`\lambda=576.3 \cdot 10^(-9) m`, the wavelength of the light

`D=8.85m`, the distance of the screen from the slits

`y_1 = 5.36 cm = 0.0536 m` is the distance of the first maximum (n=1) from the central fringe

Therefore, we can re-arrange the equation to calculate the separation between the slits:

`d= (n \lambda D)/(y_n)= ((1)(576.3 \cdot 10^(-9) m)(8.85 m))/(0.0536 m)=9.52 \cdot 10^(-5) m`