MHT CET · Physics · Waves and Sound

Two light waves of intensities $I_{1}$ and $I_{2}$ having same frequency pass through the same medium at a time in the same direction and interfere. The sum of the minimum and maximum intensities is

A $(I_{1} + I_{2})$
B $2 (I_{1} + I_{2})$
C $({\sqrt{I_{1}}}_{} + \sqrt{I_{2}})$
D $({\sqrt{I_{1}}}_{} - \sqrt{I_{2}})$

Verified Solution

Answer & Solution

Correct Answer

(B) $2 (I_{1} + I_{2})$

Step-by-step Solution

Detailed explanation

I_{max} = {(a_{1} + a_{2})}^{2}

I_{min} = {(a_{1} - a_{2})}^{2}

I_{max} + I_{min} = a_{1}^{2} + a_{2}^{2} + a_{1}^{2} + a_{2}^{2}

= 2 (a_{1}^{2} + a_{2}^{2})

= 2 (I_{1} + I_{2})

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.

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Two light waves of intensities I1 and I2 having same frequency pass through the same medium at a time in the same direction and interfere. The sum of the minimum and maximum intensities is

Step-by-step Solution

Two light waves of intensities $I_{1}$ and $I_{2}$ having same frequency pass through the same medium at a time in the same direction and interfere. The sum of the minimum and maximum intensities is