If the melanin lines on the wing are spaced 2.0 μm apart, what is the first-order diffraction angle for green light (λ = 550 nm)?

This question is incomplete, the complete question is;

The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing.

If the melanin lines on the wing are spaced 2.0 μm apart, what is the first-order diffraction angle for green light (λ = 550 nm)?

the first-order diffraction angle for green light is 15.96°

Explanation:

Given the data in the question;

from diffraction theory;

nλ = dsin∅

where n is the diffraction order ( 1st order = 1 )

λ is the wavelength ( 550 nm  = 550 × 10⁻⁹ m)

d is the grating spacing ( 2.0 μm = 2.0 × 10⁻⁶ m )

∅ is the diffraction angle ( ? )

so we substitute

nλ = dsin∅

sin∅ = nλ / d

sin∅ = (1 × 550 × 10⁻⁹ m) / 2.0 × 10⁻⁶ m

sin∅ = 0.275

∅ = sin⁻¹(0.275)

∅ = 15.96°

Therefore, the first-order diffraction angle for green light is 15.96°

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