In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $α$ as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is 11 mm. Which of the following statement (s) is/are correct ?

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Fringe spacing depends on $α$ .

For $α = \frac{0.36}{π}$ degree, there will be destructive interference at point O.

For $α = \frac{0.36}{π}$ degree, there will be destructive interference at point P.

For $α = 0$ , there will be constructive interference at point P.

answer is A.

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Detailed Solution

Total geometric path difference for point P is

$∆ x = d \sin α + \frac{y d}{D}$

For option (1),

$α = \frac{0.36}{π}$ degree

Since $α$ is small, so

$∆ x = α d + \frac{y d}{D} \Rightarrow ∆ x = 3900 n m$

Since $∆ x = 3900 n m$ is an odd multiple of $\frac{λ}{2}$ i.e., 300 nm.

$\Rightarrow (2 n - 1) \frac{λ}{2} = ∆ x$ (for destructive interference)

$\Rightarrow n = 7$

For option (2),

Fringe width in all the above case reman unchanged.

For option (3),

$∆ x_{0} = 0$ and $\frac{y d}{D} = 3300 n m$

As $(α = 0)$ (Destructive interference at P)

For option (4),

If $α = \frac{0.36}{π}$ degree

Then $∆ x_{0} = α d = 600 n m$

$\Rightarrow ∆ x_{0} = n λ$ (for n=1) (Constructive interference)

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