How Does Light Wave Interference Reveal the Width of a Spider Web?

[nophun6]

Hello, I need help with a light wave interference question.

Q: Imagine you are trying to measure the width of a single strand of spider web. You have fastened the web to the slide horizontally. You illuminate the strand with a 650nm laser and project the resulting interference pattern onto the wall where you have fastened a piece of paper. Given that the strand is
65 μm wide and is located 2 meters from the wall, draw the resulting interference pattern you would see in. Draw the pattern to scale in the correct orientation. Include only the m=-2, -1, 0, 1, 2 maxima (bright spots). Indicate the distance between each adjacent maximum.

Usually I would say what I know and how I would approach this problem, but for this one I really am at a lost. Any help is greatly appreciated

 

[lightgrav]

The spider web thread is opaque; it will cast a shadow.
Outside the edges of the thread are paths that diffract into the shadow.
They each have a path length from thread to screen (like single-slit)
the path Length difference (L_top - L_bottom) causes interference.

 

[kyle8921]

.

I would first start by understanding the concept of light wave interference. Light waves are a form of electromagnetic radiation that can exhibit wave-like properties, such as interference. Interference occurs when two or more light waves interact with each other, leading to a change in the resulting wave pattern.

In this scenario, the single strand of spider web acts as a diffraction grating, splitting the incoming laser light into multiple waves that interfere with each other. The resulting interference pattern can be seen on the wall where the light is projected.

To measure the width of the spider web, we can use the interference pattern and apply the principles of diffraction. The distance between two adjacent maxima (bright spots) in the pattern is related to the wavelength of the light and the distance between the web and the wall.

In this case, the distance between the web and the wall is 2 meters, and the wavelength of the laser light is 650nm. Using the formula d sinθ = mλ, where d is the distance between the web and the wall, θ is the angle of diffraction, m is the order of the bright spot, and λ is the wavelength, we can calculate the width of the spider web.

Assuming that the angle of diffraction is small, we can use the approximation sinθ ≈ θ and rearrange the formula to solve for the width of the web (d):

d = mλ/θ

Using this formula, we can calculate the width of the web for each of the five maxima (m = -2, -1, 0, 1, 2). The distance between each adjacent maximum will decrease as the order (m) increases, resulting in a pattern that looks like a series of decreasing triangles.

To draw the resulting interference pattern, we can use a scale where 1 cm represents 1 meter. The distance between each adjacent maximum will then be 65μm, or 0.065 cm. Starting from the central maximum (m=0), we can draw five triangles with decreasing base lengths of 0.065 cm, 0.052 cm, 0.039 cm, 0.026 cm, and 0.013 cm. These triangles represent the bright spots in the interference pattern.

In conclusion, by understanding the principles of light wave interference and applying the formula for diffraction, we can determine the width of the spider web using the resulting interference pattern. I hope