The slit of width 'b' is illuminated by light of wavelength `6000 Å` . For what value of 'b' will be first maximum fall at angle of diffraction of `30^@` ?

Explanation

To find the slit width 'b' for which the first maximum falls at an angle of diffraction of \(30^\circ\) when illuminated by light of wavelength \(6000 \, \text{Å}\), we can use the formula for the position of maxima in single-slit diffraction.

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
The given wavelength is \(6000 \, \text{Å}\). We need to convert this to meters.
\[
\lambda = 6000 \, \text{Å} = 6000 \times 10^{-10} \, \text{m} = 6000 \times 10^{-7} \, \text{m} = 6 \times 10^{-7} \, \text{m}
...