Finding Slit Separation Using the Double-Slit Apparatus

In summary, the problem involves finding the slit separation of a double-slit apparatus using the equation d sin (theta) = m* lambda, with given values for m, lambda, and theta. After making a mistake with the value for theta, the correct answer was found by adjusting for the first minimum having an m value of 0.
  • #1
patelpalak
9
0

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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  • #2
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:
 
  • #3
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 ...
 
  • #4
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:
 
  • #5
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:
  • #6
ok thanks all i got the answer...
appriciate your help...thanx once again!:smile:
 

1. What is slit separation?

Slit separation refers to the distance between two adjacent slits in an optical instrument, such as a spectrometer or a diffraction grating.

2. Why is slit separation important in scientific research?

Slit separation plays a crucial role in determining the resolution and accuracy of measurements in scientific research. It affects the amount of light passing through the instrument and can impact the precision of data collected.

3. How do you measure slit separation?

The most common method to measure slit separation is by using a ruler or caliper to physically measure the distance between the two slits. Alternatively, it can also be calculated using the known dimensions of the instrument and the number of slits present.

4. What factors can affect slit separation?

Slit separation can be affected by various factors, such as the material and thickness of the slits, the angle at which they are positioned, and any mechanical deformations or misalignments in the instrument.

5. How can I optimize slit separation for my experiment?

The optimal slit separation for an experiment depends on the specific research goals and the properties of the light source. Generally, a smaller slit separation can provide higher resolution, but it may also reduce the amount of light passing through. It is important to carefully consider the trade-offs and determine the most suitable slit separation for the desired outcome.

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