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

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The discussion revolves around solving a homework problem related to slit diffraction in water. The key equation for dark fringes in single-slit diffraction, sin(theta) = m*lambda/a, is identified, with the user noting that m = 1 and a = Y. The user seeks clarification on how immersing the apparatus in water, with an index of refraction of n=1.33, affects the wavelength of light and the resulting diffraction pattern. It is emphasized that the wavelength of light decreases in a medium with a higher index of refraction, which is crucial for calculating the distance between dark fringes. Understanding the relationship between the speed of light in different media and the wavelength is essential for solving the problem.
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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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