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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. .

Hello Muhammad,

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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