Question

Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be:

• A. 2 : 3
• B. 16 : 81
• C. 25 : 169
• D. 25 : 1

Hint:

The intensity of interference maxima and minima in an interference pattern depends on the relative intensities of the two interfering beams. Use the formulas \( I_{{max}} = I_1 + I_2 + 2\sqrt{I_1 I_2} \) and \( I_{{min}} = I_1 + I_2 - 2\sqrt{I_1 I_2} \) to calculate.

Answer 1

The Correct Option is D

Step 1: Let the intensities of the two beams be \( I_1 \) and \( I_2 \). The ratio of the intensities is given by: \[ \frac{I_1}{I_2} = \frac{9}{4}. \] Step 2: The total intensity of interference maxima and minima depends on the superposition principle. - The intensity at maxima is given by: \[ I_{{max}} = I_1 + I_2 + 2 \sqrt{I_1 I_2}. \] - The intensity at minima is given by: \[ I_{{min}} = I_1 + I_2 - 2 \sqrt{I_1 I_2}. \] Step 3: Substitute \( I_1 = 9k \) and \( I_2 = 4k \) into these equations. For maxima: \[ I_{{max}} = 9k + 4k + 2 \sqrt{9k \times 4k} = 13k + 2 \times 6k = 13k + 12k = 25k. \] For minima: \[ I_{{min}} = 9k + 4k - 2 \sqrt{9k \times 4k} = 13k - 12k = k. \] Step 4: The ratio of the intensity at maxima to minima is: \[ \frac{I_{{max}}}{I_{{min}}} = \frac{25k}{k} = 25 : 1. \] But, based on the calculation above, the correct answer is: \[ \boxed{16 : 81}. \]