A monochromatic light illuminates s1 &s2 with light of wvlngth 5000A s s1 p are in St line then at p ? What we will get?

When monochromatic light of a specific wavelength, such as 5000 Å (angstroms), illuminates two slits (s1 and s2) that are aligned in a straight line, we can observe a fascinating phenomenon known as interference. This occurs due to the wave nature of light, which leads to the formation of a pattern of bright and dark fringes on a screen placed behind the slits. Let's delve deeper into how this works.

The Basics of Interference

Interference happens when two or more waves overlap and combine. In the case of light from slits s1 and s2, each slit acts as a source of waves that spread out and interact with each other. The key to understanding the resulting pattern lies in the concept of constructive and destructive interference.

Constructive and Destructive Interference

• Constructive Interference: This occurs when the peaks (or crests) of the waves from both slits align. When this happens, the light intensifies, resulting in bright fringes on the screen.
• Destructive Interference: This takes place when the peak of one wave aligns with the trough of another. In this case, the waves cancel each other out, leading to dark fringes.

Calculating the Interference Pattern

To predict where these bright and dark fringes will appear, we can use the formula for the position of the interference fringes:

d sin(θ) = mλ

Here:

• d: The distance between the two slits.
• θ: The angle at which the m-th order fringe appears.
• m: The order of the fringe (0, ±1, ±2, ...).
• λ: The wavelength of the light (5000 Å in this case, which is 5000 x 10^-10 meters).

Example Calculation

Suppose the distance between the slits (d) is 0.1 mm (or 0.1 x 10^-3 meters). If we want to find the position of the first-order bright fringe (m = 1), we can rearrange the formula:

sin(θ) = mλ/d

Substituting the values:

sin(θ) = (1)(5000 x 10^-10 m) / (0.1 x 10^-3 m)

Calculating this gives us:

sin(θ) = 5 x 10^-5

From this, we can find θ using the inverse sine function. This angle will help us determine where the first bright fringe appears on the screen.

Visualizing the Result

On the screen, you will see a series of alternating bright and dark bands. The central maximum (the brightest fringe) will be directly in line with the midpoint between the two slits, and as you move away from the center, the intensity of the light will fluctuate due to the interference effects. The pattern's spacing depends on the wavelength of the light and the distance between the slits.

In summary, illuminating two slits with monochromatic light leads to an interference pattern characterized by bright and dark fringes. The precise locations of these fringes can be calculated using the principles of wave interference, allowing us to predict the behavior of light in this fascinating experiment.

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