Question

What is the spacing between structures in a feather that acts as a reflection grating, given that they produce a first-order maximum for 525-nm light at a 30.0º angle?

a) 1.00 μm
b) 1.25 μm
c) 1.50 μm
d) 1.75 μm

Answer 1

The spacing between structures in the feather is 1.05 μm.

Step-by-step explanation:

To find the spacing between structures in a feather that acts as a reflection grating, we can use the equation for grating diffraction:

sin(θ) = mλ/d

where θ is the angle of diffraction, m is the order of diffraction, λ is the wavelength of light, and d is the spacing between structures. In this case, we are given that the angle of diffraction is 30.0°, the wavelength of light is 525 nm, and we want to find d. Taking the sine of both sides and rearranging the equation, we get:

d = mλ/sin(θ)

Plugging in the values, we have:

d = (1)(525 x 10^-9 m)/sin(30.0°)

d = 1.05 x 10^-6 m = 1.05 μm

Therefore, the spacing between structures in the feather is 1.05 μm.