Calculating slit width by length difference of 1st and 2nd minima

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Homework Help Overview

The problem involves calculating the slit width in a diffraction scenario, given the wavelength, distance to the screen, and the distance between the first and second minima on the screen. The subject area is wave optics, specifically related to interference patterns created by slits.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relevant equations for minima and the relationship between angles and distances on the screen. There is an exploration of how to express the positions of the minima and the implications of small angle approximations.

Discussion Status

Some participants have provided guidance on setting up equations for the positions of the minima and suggested finding the difference between these positions. Others are questioning the relationships between angles for different minima and expressing confusion about the correct approach to take.

Contextual Notes

There is a mention of specific values for wavelength, distance to the screen, and the distance between minima, which are critical for solving the problem. Participants are also navigating the constraints of using small angle approximations.

Unemployed
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Homework Statement


What is the slit width? Wavelength is 635 nm. Distance between screen and slit, 2.5 m. Distance on screen between first and second minima above the central maxima is delta 6 mm.


Homework Equations



D* sin theta * = m * lambda

tan theta = x/ distance between screen and slit



The Attempt at a Solution



I set lambda/sin theta m2-sin theta m1= 2*lambda/ sin theta m2

tan theta 2m = x + 6 *10^-3 m/2.5

I tried to plug it in, but i got stuck. What's the correct approach?
 
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Hi Unemployed, welcome to PF.
You have given the relevant equations. Now what is the condition for minimum on the screen? Write down two equations for x values.. One for first minimum and other for second minimum. Then find the difference between the x values. x2 - x1 value is given. Find D.
 
x1 = tan theta m1*2.5
x2 = (tan (theta m1 + theta m2) *2.5) + 6 *10^-3

Is theta for m2 half of what it is for m1?

Still puzzled.
 
for small angle sin θ can be written as tan θ = x/D, where x os the distance between screen and slit. Put m = 1 for first minimum and m = 2 for second minimum. Find x1 and x2. Difference between x1 and x2 is given. Find slit width d using the formula x/D = m*λ/d
 

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