Single-Slit Diffraction and the Effect of Refractive Index on Central Peak Width

In summary, the question asks whether the width of the central peak in single-slit diffraction would change if the entire apparatus were submerged in water. The width of the slit in air is 170 micrometers, and the index of refraction changes from 1 to 1.33 when submerged in water. This means the wavelength of the laser light would decrease, causing the width of the central peak to also decrease. The width can be calculated using the equation asin(theta) = m(lambda), where lambda is the new wavelength in water.
  • #1
fubag
105
0
[SOLVED] Single-Slit Diffraction

Homework Statement


You have been asked to measure the width of a slit in a piece of paper. You mount the paper 80.0 centimeters from a screen and illuminate it from behind with laser light of wavelength 633 nanometers (in air). You mark two of the intensity minima as shown in the figure, and measure the distance between them to be 17.9 millimeters.

If the entire apparatus were submerged in water, would the width of the central peak change?

a.The width would increase.
b.The width would decrease.
c.The width would not change.


Homework Equations



asin(theta) = m(lambda)



The Attempt at a Solution



Well for the first part of this question I found the width of this slit in air to be 170 micrometers.

I know this is a conceptual question, but I need help understanding exactly what happens. I know the index of refraction changes from 1 to 1.33.
 
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  • #2
Hi fubag,

When the apparatus is underwater, what will change about the light?
 
  • #3
lamda would change by a factor of decreasing 1.33 so the width would decrease therefore?
 
  • #4
how do you calculute "width of the central peak"? Put the new lambda there.
 
  • #5
ok thanks a lot!
 

1. What is single-slit diffraction?

Single-slit diffraction is a phenomenon that occurs when a single slit is placed in front of a light source. The slit acts as a barrier, causing the light to spread out and create a pattern of light and dark fringes on a screen placed behind it.

2. What causes single-slit diffraction?

Single-slit diffraction is caused by the interference of light waves as they pass through the narrow opening of the slit. This interference causes the light to spread out and create a diffraction pattern.

3. What factors affect the diffraction pattern in single-slit diffraction?

The width of the slit, the wavelength of the light, and the distance between the slit and the screen are the main factors that affect the diffraction pattern in single-slit diffraction. Additionally, the shape of the slit and the intensity of the light can also have an impact on the pattern.

4. How is single-slit diffraction different from double-slit diffraction?

Single-slit diffraction occurs when light passes through a single narrow opening, while double-slit diffraction occurs when light passes through two parallel narrow openings. In single-slit diffraction, the resulting pattern is a central bright spot with alternating light and dark fringes on either side. In double-slit diffraction, the resulting pattern is a series of bright and dark bands.

5. What are the practical applications of single-slit diffraction?

Single-slit diffraction is commonly used in fields such as optics, astronomy, and microscopy. It can be used to measure the wavelength of light, study the properties of materials, and create diffraction gratings for various purposes. It also plays a role in the development of new technologies, such as diffraction-based sensors and devices.

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