Interference fringes are produced on a screen by using two light sources of intensities I and 9I. The phase difference between the beams is π2 at the point P and π at the point Q on the screen. The difference between the resultant intensities at point P and Q is

MHT CET · Physics · Waves and Sound

Interference fringes are produced on a screen by using two light sources of intensities $I$ and $9 I$ . The phase difference between the beams is $\frac{π}{2}$ at the point $P$ and $π$ at the point $Q$ on the screen. The difference between the resultant intensities at point $P$ and $Q$ is

A $2 I$
B $4 I$
C $6 I$
D $8 I$

Verified Solution

Answer & Solution

Correct Answer

(C) $6 I$

Step-by-step Solution

Detailed explanation

At point P, resultant intensity of interfering wave is

{(I_{P})}_{r e s} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos θ

For

θ = \frac{π}{2}, {(I_{P})}_{r e s} = I + 9 I = 10 I

At point Q, resultant intensity of interfering wave is

{(I_{Q})}_{r e s} = 10 I - 2 . \sqrt{9 I^{2}} = 10 I - 6 I = 4 I

for

θ = π

∴ ∆ I = {(I_{P})}_{r e s} - {(I_{g})}_{r e s} = 10 I - 10 I + 6 I = 6 I

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Match the column-I with column-II and select the correct option.

	Column I (Traits)		Column II (Type of inheritance)
i.	Roan cattle	a.	Multiple allelism
ii.	Pink flowered Mirabilis jalapa plant	b.	Co-dominance
iii.	Sickle cell anaemia	c.	Incomplete dominance
iv.	Wings in Drosophila	d.	Pleiotropism

MHT CET 2023 Hard

Explore more questions on app