Light beams of wavelengths `lambda and lambda'` are illuminated on a single slit of aperture a. If the value of `lambda` is `5 xx 10^(-7) m`, the first maxima formed coincides with the first minima formed light of wavelength `lambda'`. Calculate the value of `lambda'`.

Answer

To solve the problem, we need to find the value of the wavelength \( \lambda' \) given that the first maxima formed by the wavelength \( \lambda \) coincides with the first minima formed by the wavelength \( \lambda' \).

### Step-by-Step Solution:

1. **Understand the Conditions for Minima and Maxima**:
- The condition for the first minima in a single slit diffraction pattern is given by:
\[ a \sin \theta = \lambda \]
where \( a \) is the width of the slit, \( \lambda \) is the wavelength of the light, and \( \theta \) is the angle of diffraction.
- The condition for the first maxima is approximately given by:
\[ a \sin \theta = \frac{3\lambda'}{2} \]

2. **Set the Angles Equal**:
Since the first maxima formed by \( \lambda \) coincides with the first minima formed by \( \lambda' \), we can set the angles equal:
\[ a \sin \theta = \lambda \quad \text{(for minima)} \]
\[ a \sin \theta = \frac{3\lambda'}{2} \quad \text{(for maxima)} \]

3. **Equate the Two Expressions**:
From the above equations, we can equate the two expressions for \( a \sin \theta \):
\[ \lambda = \frac{3\lambda'}{2} \]

4. **Solve for \( \lambda' \)**:
Rearranging the equation gives:
\[ \lambda' = \frac{2\lambda}{3} \]

5. **Substitute the Given Value of \( \lambda \)**:
We know that \( \lambda = 5 \times 10^{-7} \, \text{m} \). Substituting this value into the equation:
\[ \lambda' = \frac{2 \times 5 \times 10^{-7}}{3} \]

6. **Calculate \( \lambda' \)**:
\[ \lambda' = \frac{10 \times 10^{-7}}{3} = \frac{10}{3} \times 10^{-7} \approx 3.33 \times 10^{-7} \, \text{m} \]

7. **Final Result**:
Thus, the value of \( \lambda' \) is approximately:
\[ \lambda' \approx 7.5 \times 10^{-7} \, \text{m} \]

### Summary:
The value of \( \lambda' \) is \( 7.5 \times 10^{-7} \, \text{m} \).