Question

Two coherent waves of intensities \(I_1\) and \(I_2\) pass through a region at the same time in the same direction. The sum of maximum to minimum intensities is

• A. \( I_1 + I_2 \)
• B. \( 2(I_1 + I_2) \)
• C. \( 2(\sqrt{I_1} + \sqrt{I_2})^2 \)
• D. \( (I_1 + I_2)^2 \)

Hint:

Always remember: \(I_{\max} + I_{\min} = 2(I_1 + I_2)\) and \(I_{\max} - I_{\min} = 4\sqrt{I_1 I_2}\).

Answer 1

The Correct Option is B

Step 1: Expression for maximum intensity.
\[ I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2 \]

Step 2: Expression for minimum intensity.
\[ I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2 \]

Step 3: Add the two intensities.
\[ I_{\max} + I_{\min} = (\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2 \]

Step 4: Expand both terms.
\[ = I_1 + I_2 + 2\sqrt{I_1 I_2} + I_1 + I_2 - 2\sqrt{I_1 I_2} \]

Step 5: Simplify expression.
\[ I_{\max} + I_{\min} = 2I_1 + 2I_2 \]
\[ I_{\max} + I_{\min} = 2(I_1 + I_2) \]

Step 6: Final conclusion.
\[ \boxed{2(I_1 + I_2)} \] Hence, correct answer is option (B).