Finding Slit Separation Using the Double-Slit Apparatus

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The discussion revolves around calculating the slit separation in a double-slit apparatus using the equation d sin(theta) = m * lambda. The user initially misapplied the formula by not converting the angle from degrees to radians, which led to an incorrect result. Another participant pointed out that for dark fringes, the correct formula should be dsin(theta) = (m + 0.5)lambda. After addressing these issues, the user successfully found the correct answer with assistance from others. The importance of proper unit conversion and understanding the fringe order in calculations was emphasized.
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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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