A Simple Study of Position of Bright Fringes

In this simple study, the position of bright fringes is analyzed when a laser beam interacts with a wave. The laser beam is passed through two slits in order to create a wave interference pattern on a screen. By varying the distance between the slits, the position of the bright fringes can be changed. This experiment allows us to see how the wave behaves when it encounters different obstacles in its path.

What Are Bright Fringes?

Bright fringes are the light and dark bands that are seen when two laser beams intersect. They occur because of wave interference. When two waves meet, they interact with each other. The strength of this wave interaction depends on the phase difference between the waves.

If the phase difference is zero, then the waves reinforce each other and a bright fringe is seen. If the phase difference is 180 degrees, then the waves cancel each other out and a dark fringe is seen. The position of the fringes depends on the path difference between the two beams of light.

So, how can we use this to study positions? Let us learn this in the underlying situation.

How Can We Study The Position Of Fringes?

By changing the path length of one of the laser beams, we can observe the movement of the fringes. By measuring the position of the fringes, we can calculate the path difference and hence the position of the laser beam.

This technique is called laser interferometry and it is used in a variety of applications such as measuring very small distances, detecting gravitational waves and measuring tiny movements.

In this experiment, we will use laser interferometry to study the position of a laser beam. We will shine two laser beams onto a screen and measure the position of the fringes. By changing the path length of one of the laser beams, we will observe the movement of the fringes. From this, we can calculate the path difference and hence the position of the laser beam.

Solved Question on  Position of Bright Fringes

Question: Calculate the position of the first and second bright fringes for laser light (wavelength = 650 nm) passing through a rectangular aperture that is 0.250 mm wide.

When light waves interact with an object, like a laser beam passing through a narrow slit, they produce a pattern of bright and dark regions called interference fringes. The position of these fringes can be determined by solving the wave equation for the laser light.

For this particular problem, we have given the width of the slit (0.250 mm) and the wavelength of the laser light (650 nm). We can use these values to calculate the position of the first and second bright fringes using the equation:

position = (width * fringe number) / wavelength

Plugging in the values from our problem, we get:

first bright fringe position = (0.250 mm * 0) / 650 nm = 0 mm

second bright fringe position = (0.250 mm * -30) / 650 nm = -15 mm

So, the position of the first bright fringe is 0 mm from the centre of the slit and the second bright fringe is 15 mm from the centre.

This question can be extended to finding the positions of all the bright fringes. In general, the equation for determining interference fringe position is:

position = (width * fringe number) / wavelength

where width is the width of the slit, the fringe number is the number of the interference fringe (starting from 0 for the first bright fringe), and wavelength is the wavelength of the laser light.

This equation can be used to solve for any interference fringe position, making it a useful tool for understanding wave behaviour.

Conclusion

The position of the bright fringes is determined by the path length difference between the two laser beams. If the path length difference is an integer multiple of the wavelength (λ) of the laser light, then constructive interference will occur and a bright fringe will be seen. If the path length difference is not an integer multiple of λ, then destructive interference will occur and a dark fringe will be seen.

This experiment can be used to determine the wavelength of laser light. By measuring the position of the bright fringes, the path length difference (ΔL) can be determined. The wavelength of the laser light can then be calculated using the equation: λ = ΔL/n, where n is an integer.

This experiment can also be used to determine the refractive index of a material. By measuring the position of the bright fringes, the path length difference (ΔL) can be determined.