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Light with a wavelength of λ = 614 nm is shone first on a single slit of width w = 3.75 μm. The single slit is then replaced with a double slit separated by a distance w. The ratio of the single slit angle to the double slit angle for the first dark fringe is Rθ.Find the ratio between these angles numerically.

User Elzell
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1 Answer

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Answer:

The ratio,
R_(\theta) is 2

Solution:

As per the question:

Wavelength,
\lambda = 614\ nm = 614* 10^(- 9)\ m

Single slit width, w =
3.75\ mu m

Now,

We know from the eqn for diffraction:


n\lambda = wsin\theta

Now,

For single slit:

n = 1


\lambda = wsin\theta_(s)


sin\theta = (\lambda)/(w)

For very small angle:


sin\theta
\theta


\theta = (\lambda)/(w) (1)

For double slit:

n = 2

Thus


2\lambda = wsin\theta_(s)


sin\theta' = (\lambda)/(2w)

For very small angle:


sin\theta
\theta


\theta' = (\lambda)/(2w) (2)

For the ratio,
R_(\theta), we divide en (1) by eqn (2):


R_(\theta) = ((\lambda)/(w))/((\lambda)/(2w)) = 2

User NamingException
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