Young's Double-Slit Problem

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In summary, in a Young's double slit experiment with a thin sheet of mica placed over one of the slits, the center of the fringe pattern shifts by 30 bright fringes. The wavelength of light is 480 nm and the index of refraction of the mica is 1.60. To account for the additional phase difference when the mica is placed, one must consider the thickness of the mica. By setting the phase difference equal to 30 wavelengths and using the fact that the number of wavelengths that fit into a thickness t depends on the index of refraction, the thickness of the mica can be calculated as t = 30λ/(n-1).
  • #1
Potatochip911
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Homework Statement


In a young's double slit experiment a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern shifts by 30 bright fringes. The wavelength of light in the experiment is 480 nm and the index of refraction of the mica is 1.60. The thickness of the mica is?

Homework Equations


##d\sin\theta=m\lambda\\
\lambda_{n}=\frac{\lambda}{n}##

The Attempt at a Solution


Without considering the effect of the mica we have that the phase difference between the slits will be ##30\lambda## however I am stuck trying to figure out how to account for the additional phase difference when the mica is placed.
 
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  • #2
Remember how one obtains ##d \sin{\theta} = m\lambda##. One initially writes down the general formula (with certain approximation) for the phase difference between the rays emanating from each slit at the distant screen. How would you modify this expression of the phase difference if one source (slit) is retarded due to the presence of a thin material? Hint: in the absence of the thin material, the phase difference between the two rays from both sources at distant screen is ##\frac{2\pi}{\lambda}d \sin{\theta}##.
 
  • #3
Potatochip911 said:

Homework Statement


In a young's double slit experiment a thin sheet of mica is placed over one of the two slits. As a result, the center of the fringe pattern shifts by 30 bright fringes. The wavelength of light in the experiment is 480 nm and the index of refraction of the mica is 1.60. The thickness of the mica is?

Homework Equations


##d\sin\theta=m\lambda\\
\lambda_{n}=\frac{\lambda}{n}##

The Attempt at a Solution


Without considering the effect of the mica we have that the phase difference between the slits will be ##30\lambda## however I am stuck trying to figure out how to account for the additional phase difference when the mica is placed.
Consider a thickness t. How many wavelengths would fit into this thickness if the region was filled with air? How many would fit into this thickness if the region was filled with mica?
 
  • #4
Thanks for the help guys, finally managed to solve it. $$PD=30\lambda \\
PD=(\frac{t}{\lambda n}-\frac{t}{\lambda})\cdot\lambda \\
30\lambda=t_{n}-t \\
t=\frac{30\lambda}{n-1} $$
This ended up giving the correct answer.
 

What is Young's Double-Slit Problem?

Young's Double-Slit Problem is an experiment that demonstrates the wave nature of light by passing a single beam of light through two parallel slits and observing the resulting interference pattern on a screen.

Who discovered Young's Double-Slit Problem?

Thomas Young, an English physicist, is credited with discovering and first explaining the phenomena of Young's Double-Slit Problem in 1801.

What is the significance of Young's Double-Slit Problem?

The significance of Young's Double-Slit Problem lies in its ability to prove the wave-like nature of light, which was a major breakthrough in the understanding of light and electromagnetic radiation. It also paved the way for the development of the wave theory of light and the concept of interference.

What are the key components of Young's Double-Slit Experiment?

The key components of Young's Double-Slit Experiment include a coherent light source, two parallel slits, and a screen to observe the interference pattern. Other important elements include a diffraction grating, which can be used instead of the two slits, and a source of monochromatic light, which produces a single color of light.

What are the practical applications of Young's Double-Slit Problem?

Young's Double-Slit Problem has practical applications in many fields, including optics, physics, and engineering. It is used to study the properties of light, such as wavelength and intensity, and is also used in the development of optical instruments, such as telescopes and microscopes. Additionally, the principles of Young's Double-Slit Problem are utilized in technologies such as holography and diffraction gratings used in spectrometers.

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