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)?
Answer:
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°
