Two wavelengths of sodium light 590 nm and 596 nm are used, in turn, to study the diffraction taking place at a single slit of aperature `2 xx 10^(-4) m`. The distance between the slit and the screen is 1.5 m. Calcualate the separation between the positions of first maximum of the diffractions patterns obtained in two cases.

Explanation

To solve the problem, we need to calculate the separation between the positions of the first maximum of the diffraction patterns obtained with two different wavelengths of sodium light. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Wavelengths of sodium light:
- \( \lambda_1 = 590 \, \text{nm} = 590 \times 10^{-9} \, \text{m} \)
- \( \lambda_2 = 596 \, \text{nm} = 596 \times 10^{-9} \, \text{m} \)
- Aperture of the slit:
- \( a = 2 \times 10^{-4} \, \text{m} \)
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