Finding Slit Separation Using the Double-Slit Apparatus

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Homework Help Overview

The problem involves determining the slit separation in a double-slit apparatus using the wavelength of light from gaseous mercury and the angle of the fifth dark fringe.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the equation d sin(theta) = m * lambda to find the slit separation but encounters difficulties with the calculations. Some participants suggest reviewing the calculations and converting angles to radians. Others question the appropriateness of the equation for dark fringes, proposing an alternative equation for dark fringe positions.

Discussion Status

The discussion includes attempts to clarify the calculations and assumptions regarding the use of radians versus degrees. Participants are exploring different interpretations of the problem, particularly regarding the equation for dark fringes. There is no explicit consensus, but guidance has been offered regarding the angle conversion and the correct application of the equation.

Contextual Notes

Participants note the need to convert the angle from degrees to radians and discuss the implications of using the correct equation for dark fringes, indicating potential misunderstandings in the setup of the problem.

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Homework Statement



The green line of gaseous mercury at 546nm fals on a double-slit apparatus.
If the fifth dark fringe is at 0.150 degree from the centerline, what is the slit separaton?


Homework Equations



d sin (theta) = m* lambda

The Attempt at a Solution



ok i used the above equatiob to find the d, slit separation
as d=m*lambda/sin(theta)

but I am getting the wrong answer...and I am not able to figure out the problem...plez
som1 help...!
 
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Hi patelpalak! :smile:

(have a lambda: λ and a theta: θ :wink:)

Show us your full calculations, and then we can see what went wrong, and we'll know how to help! :smile:
 
ok here's what i did

d sin (theta) =m*lamdba

therefore, d=m*lambda/ sin(theta)

m=5, since its fifth fringe
lambda= 546*10^-9
theta = 0.150 degrees

so, d=(5)(546*10^-9)/sin(0.150)

and i get 0.001042 meters
but it gives me wrong answer...!
thats all i did ...
 
Hi patelpalak! :smile:

(whatever happened to that λ and θ I gave you? :confused:)
patelpalak said:
ok here's what i did

d sin (theta) =m*lamdba

theta = 0.150 degrees

so, d=(5)(546*10^-9)/sin(0.150)

erm :redface: … θ has to be in radians! :wink:
 
Hmmm... If it is a dark fringe, isn't the equation something like:

dsinθ = (m+0.5)λ

?

Also, if my memory serves me correctly, you need to be careful with the order of your minimum. The first minimum has an m value of 0.
 
Last edited:
ok thanks all i got the answer...
appriciate your help...thanx once again!:smile:
 

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