Question

A slit of width ‘a’ is illuminated by red light of wavelength 6500 A°. If the first diffraction minimum falls at 30°, then the value of ‘a’ is ________

• A. 6.5 × 10^-4 mm
• B. 1.3 micron
• C. 3250 A°
• D. 2.6 × 10^-4 cm

Answer 1

The Correct Option is B

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).