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# Physics/young's double slit

Question
In a young's double slit experiment ,light of wavelength 5k angstrom illuminates two slits which are seperated by1mm.calculate the seperation between  adjacent bright fringes on a screen 5 m away from slits. .

The formula for the case of maxima on the screen is
d*sin(theta) = m*lambda,
where m is 1,2,3,... and lambda is the wavelength of the light. To identify what the other variables (d and theta) represent, please go to
http://web.mit.edu/viz/EM/visualizations/coursenotes/modules/guide14.pdf
and scroll to Figure 14.2.3.
Our data is that
d = 1*10^-3 m and
lambda = 5k angstrom * (10^-10 m / 1 angstrom) = 5*10^-6 m

We can rearrange the formula to
sin(theta) = m*lambda / d
Let us examine the maxima with m=1 and m=2.

m=1:
sin(theta) = 1 * 5*10^-6 m / 1*10^-3 m = 5*10^-3
Since the angle is so small, we can use these approximations:
sin(theta) = tan(theta) = theta (in radians).

We will now do some trigonometry using the approximations above.
tan(theta) = y/L and therefore
y = L*tan(theta)
where y and L are as used in Figure 14.2.3.
y = 5 m * 5*10^-3 = 25*10^-3 = 25 mm

m=2:
sin(theta) = 2 * 5*10^-6 m / 1*10^-3 m = 10*10^-3
Repeating the trigonometry in m=1 above,
y = L*tan(theta) = 5 m * 10*10^-3 = 50*10^-3 = 50 mm

So we see that adjacent maxima are 25 mm apart.
You may be interested in the calculator provided in this web site:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html

I hope this helps,
Steve
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Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University