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Red light of wavelength 6500 Å illuminates a single slit of width a. If the first diffraction minimum occurs at θ = 30°, what is the slit width a?

1. 3250 Å
2. 6.5 × 10⁻⁴ mm
3. 1.3 micron
4. 2.6 × 10⁻⁴ cm

Correct answer: 1.3 micron

Solution

The condition for the first minimum in single-slit diffraction is a*sin(θ) = λ. With θ = 30°, sin(θ) = 0.5, so a = λ/0.5 = 2λ = 2 × 6500 Å = 13000 Å = 1.3 × 10⁻⁶ m = 1.3 micron.

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