A lens of focal length `1m` forms Fraunhofer diffraction pattern of a single slit of width `0.04 cm` in its focal plane. The incident light contains two wavelength `lambda_(1)` and `lambda_(2)`. It is found that the fourth minimum corresponding to `lambda_(1)` and the fifth minimum corresponding to `lambda_(2)` occur at the same point `0.5 cm` from the central maximum. Compute `lambda_(1)` and `lambda_(2)`

Explanation

To solve the problem, we need to find the wavelengths \( \lambda_1 \) and \( \lambda_2 \) based on the given information about the Fraunhofer diffraction pattern produced by a single slit. Here’s a step-by-step solution:

### Step 1: Understand the given parameters
- Focal length of the lens, \( f = 1 \, \text{m} \)
- Width of the slit, \( D = 0.04 \, \text{cm} = 0.04 \times 10^{-2} \, \text{m} = 4 \times 10^{-4} \, \text{m} \)
- Position of the minima from the central maximum, \( y = 0.5 \, \text{cm} = 0.5 \times 10^{-2} \, \text{m} = 5 \times 10^{-3} \, \text{m} \)

### Step 2: Use the formula for minima in single-slit diffraction
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