Slit Diffraction in Water: Solving for the Distance Between Dark Fringes

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SUMMARY

The discussion focuses on calculating the distance between dark fringes in a single-slit diffraction pattern when the apparatus is immersed in water, with a refractive index of 1.33. The relevant equation for dark fringes is given by sin(theta) = m * lambda / a, where m is the order of the fringe and a is the slit width. The wavelength of light in the medium is affected by the index of refraction, which alters the effective wavelength used in the diffraction calculations. The user seeks clarification on how to incorporate the refractive index into their calculations.

PREREQUISITES
  • Understanding of single-slit diffraction principles
  • Familiarity with the equation for dark fringes in diffraction
  • Knowledge of the relationship between wavelength and index of refraction
  • Basic concepts of light behavior in different media
NEXT STEPS
  • Research how to calculate the effective wavelength of light in a medium using the index of refraction
  • Study the derivation of the single-slit diffraction formula
  • Explore practical applications of diffraction in optical systems
  • Learn about the effects of different media on light propagation and diffraction patterns
USEFUL FOR

Students studying optics, physics educators, and anyone interested in understanding the effects of medium on light diffraction patterns.

sghaussi
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slit diffraction in water?

Hello! I'm having trouble answer this homework problem:

Suppose the entire apparatus (light of wavelength X nm from a distant source is incident on a slit Y mm wide, and the resulting diffraction pattern is observed on a screen Z m away) is immersed in water (n=1.33).

Then what is the distance between the two dark fringes on either side of the central bright fringe?

I know what I want to use the equation for Dark fringes in single-slit diffraction:
sin(theta) = m*lamda/a

in my case, m = 1
and a = y

I'm not sure how to solve this problem now that the entire apparatus is immersed in water? I know water affects this, but how? Can you help me start this problem?
 
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How does the wavelength of light depend on the index of refraction of the medium?
 
thanks! i knew it was a concept I had studied a few chaptes earlier but it completely slipped my mind. that's right, index of refraction depends on c and hte speed of light in that particular medium! =)
 

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