Two wavelengths of sodium light 590 nm and 596 nm are used , in turn, to study the diffraction taking place due to a single slit of aperture `1xx10^(-4)m`. The distance between the slit and the screen is 1.8m. Calculate the separation between the positions of the first maxima of the diffraction pattern obtained in the two cases.

Explanation

To solve the problem step by step, let's break down the calculations involved in determining the separation between the positions of the first maxima of the diffraction pattern for the two wavelengths of sodium light.

### Step 1: Convert Wavelengths to Meters
The given wavelengths of sodium light are:
- \( \lambda_1 = 590 \, \text{nm} = 590 \times 10^{-9} \, \text{m} = 5.90 \times 10^{-7} \, \text{m} \)
- \( \lambda_2 = 596 \, \text{nm} = 596 \times 10^{-9} \, \text{m} = 5.96 \times 10^{-7} \, \text{m} \)

### Step 2: Identify Given Values
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