Using the diffraction formula for the first minimum:
\[ a \sin \theta = n \lambda \]
Given:
\[ \theta = 30°, \quad n = 1, \quad \lambda = 6500 \, \text{Å} = 6.5 \times 10^{-7} \, \text{m} \]
Substitute the values:
\[ a \sin 30° = 6.5 \times 10^{-7} \, \text{m} \]
\[ a = \frac{6.5 \times 10^{-7} \, \text{m}}{0.5} = 1.3 \times 10^{-6} \, \text{m} \]
Convert to microns:
\[ a = 1.3 \, \text{micron} \]
Thus, the correct answer is Option (B).
Step 1: Identify Formula
Condition for first diffraction minimum: $a \sin\theta = \lambda$
Step 2: List Given Values
$\lambda = 6500 \ A°$
$\theta = 30°$
Step 3: Substitute Values
$a \sin(30°) = 6500 \ A°$
Step 4: Solve for 'a'
$a = \frac{6500 \ A°}{\sin(30°)} = \frac{6500 \ A°}{1/2} = 13000 \ A°$
Step 5: Convert to meters
$a = 13000 \times 10^{-10} \ m = 1.3 \times 10^{-6} \ m$
Step 6: Convert to microns
$a = 1.3 \times 10^{-6} \ m = 1.3 \ micron$
Final Answer: The final answer is $1.3 \ micron$