A diffraction grating has a spacing of 5 µm. A monochromatic light of wavelength 650 nm falls on it. Calculate the angle θ (in degrees) at which the third order maximum (m = 3) appears.
Answer
22.9° (approximately)
The correct answer is 22.9° (approximately) — Compute θ: θ = sin⁻¹(0.39) ≈ 22.9°.
Step-by-step solution
- Use diffraction grating equation: d sinθ = mλ.
- Convert d to metres: 5 µm = 5×10⁻⁶ m.
- Convert λ to metres: 650 nm = 6.5×10⁻⁷ m.
- Insert m = 3: sinθ = (3×6.5×10⁻⁷)/(5×10⁻⁶) = 0.39.
- Compute θ: θ = sin⁻¹(0.39) ≈ 22.9°.
Common mistake: Omitting the order number m or mixing up units
Concept tested: Diffraction grating equation
Published · How this solution was prepared and checked
← All Wave Optics questions