Perhaps to confuse a predator, some tropical gyrinid beetles(whirligig beetles) are colored by optical interference that is dueto scales whose alignment forms a diffraction grating (whichscatters light instead of transmitting it). when the incident lightrays are perpendicular to the grating, the angle between thefirst-order maxima (on opposite sides of the zeroth-order maximum)is about 30° in light with a wavelength of 589 nm. what is thegrating spacing of the beetle?

The grating spacing of the beetle is

Explanation:

The concept to solve this problem is relate to interference effect given in the Young's Slits. Here was demonstrated that the length of the side labelled \lambda is known as the path difference. The equation is given by,

Where,

= wavelenght of light

N = a positive integer: 1,2,3...

= Angle from the center of the wall to the dark spot

d= width of the slit

Replacing our values we have that for n=1,

Therefore the grating spacing of the beetle is