Final answer:
The spacing between structures in a feather that acts as a reflection grating can be determined using the grating equation. For a first-order maximum with 525 nm light at a 30.0° angle, the spacing between structures in the feather is approximately 1.05 micrometers.
Step-by-step explanation:
The spacing between structures in a feather that acts as a reflection grating can be determined using the formula for the grating equation: dsin(theta) = m * lambda, where d is the spacing between the structures, theta is the angle of diffraction, m is the order of maximum, and lambda is the wavelength of light.
In this case, we are given that the angle of diffraction is 30.0°, the order of maximum is 1, and the wavelength of light is 525 nm. Substituting these values into the grating equation, we can solve for d:
d * sin(30.0°) = 1 * 525 nm
d = 1 * 525 nm / sin(30.0°)
The spacing between structures in the feather is approximately 1050 nm, or 1.05 micrometers.