SATHEE: Optics Question 163

Optics Question 163

Question: Two coherent sources S1 and S2 are separated by a distance four times the wavelength l of the source. The sources lie along y axis whereas a detector moves along + x axis. Leaving the origin and far off points the number of points where maxima are observed is

Options:

A) 2

B) 3

C) 4

D) 5

Show Answer

Answer:

Correct Answer: B

Solution:

From $Δ S_{1} S_{2} D,$

${(S_{1} D)}^{2} = {(S_{1} S_{2})}^{2} + {(S_{2} D)}^{2}$

${(S_{1} P + P D)}^{2} = {(S_{1} S_{2})}^{2} + {(S_{2} D)}^{2}$ .

Here $S_{1} P$ is the path difference $= n λ$ for maximum intensity.

$∴ {(n λ + x_{n})}^{2} = {(4 λ)}^{2} + {(x_{n})}^{2}$ or $x_{n} = \frac{16 λ^{2} - n^{2} λ^{2}}{2 n λ}$ .

Then $x_{1} = \frac{16 λ^{2} - λ^{2}}{2 λ} = 7.5 λ$

$x_{2} = \frac{16 λ^{2} - 4 λ^{2}}{4 λ} = 3 λ$

$x_{3} = \frac{16 λ^{2} - 9 λ^{2}}{6 λ} = \frac{7}{6} λ$

$x_{4} = 0$ .

$∴$ Number of points for maxima becomes 3.

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Optics Question 163

Question: Two coherent sources S1 and S2 are separated by a distance four times the wavelength l of the source. The sources lie along y axis whereas a detector moves along + x axis. Leaving the origin and far off points the number of points where maxima are observed is

Options:

Answer:

Solution:

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