Question

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 apart, what is the first-order diffraction angle for green light (lamda=550 nm)?

Answer 1

15.96°

Step-by-step explanation:

n = Diffraction order = 1

`\lambda` = Wavelength = 550 nm

d = Grating space =
`2\mu m` (generally given in
`\mu m`)

`\theta` = Diffraction angle

From diffraction theory we have the relation

`n\lambda=dsin\theta`

`\theta=sin^(-1)(n\lambda)/(d)\\\Rightarrow \theta=sin^(-1)(1* 550* 10^(-9))/(2* 10^(-6))\\\Rightarrow \theta=15.96^(\circ)`

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