Double Slit Interference and linear distance

[rachiebaby17]

Homework Statement

In a double-slit interference experiment, the wavelength is 579 nm, the slit separation is 0.12 mm, and the screen is 30.0 cm away from the slits. What is the linear distance between adjacent maxima on the screen? [Hint: Assume the small angle approximation is justified and then check the validity of your assumption once you know the value of the separation between adjacent maxima.]

Homework Equations

where
λ is the wavelength of the light,
d 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=0),
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

The Attempt at a Solution

Again I'm completely lost, some hints on how to start would be great

 

[rl.bhat]

Write down the equation for xn, linear distance of the nth bright fringe from central maximum and similarly for x(n-1) of (n-1)th bright fringe. The difference between these will be the required result.

 

[nlightner]

I can provide some guidance on how to approach this problem. First, you need to understand the concept of double-slit interference and how it works. In this experiment, we are using light of a specific wavelength (579 nm) and passing it through two slits that are separated by 0.12 mm. The light then hits a screen that is 30.0 cm away from the slits. The question asks for the linear distance between adjacent maxima on the screen.

To solve this problem, we can use the equation given in the homework statement: x = λL/d. This equation relates the distance between the bands of light (x) to the wavelength of the light (λ), the distance from the slits to the screen (L), and the separation of the slits (d). We can rearrange this equation to solve for d: d = λL/x.

To use this equation, we need to know the value of x, which is the distance between adjacent maxima on the screen. This can be calculated by using the small angle approximation, which states that for small angles, the tangent of the angle is approximately equal to the angle itself. In this case, we can assume that the angle between adjacent maxima is small, so we can use the equation tanθ = x/L, where θ is the angle between adjacent maxima.

Once we have the value of x, we can plug it into our original equation to solve for d. However, we should also check the validity of our assumption of small angles. If the angle is not small, then we would need to use a more complex equation to solve for x and d.

In summary, to solve this problem, we need to understand the concept of double-slit interference, use the small angle approximation to calculate the distance between adjacent maxima on the screen, and then use the equation d = λL/x to find the linear distance between adjacent maxima.