#2 and 3
Perhaps to confuse a predator, some tropical beetles are collared by optical interference...
Perhaps to confuse a predator, some tropical beetles are collared by optical interference that is due to scales whose alignment forms a diffraction grating (which scatters light instead of transmitting it). When the incident light rays are perpendicular to the grating, the angle between the first-order maxima (on opposite sides of the zeros-order maximum) is 31degree in light with a wavelength of 550 nm. What is the grating spacing of the beetle? What is the smallest Bragg angle for x-rays of wavelength 24 pm to reflect from reflecting planes spaced 0.24 nm apart in a calcite crystal?