Question

Perhaps to confuse a predator, some tropical gyrinid beetles (whirligig beetles) are colored 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 zeroth-order maximum) is about 27° in light with a wavelength of 534 nm. What is the grating spacing of the beetle?

Answer 1

the grating space is given as

`a = 3.43 * 10^(-6) m`

Step-by-step explanation:

As we know that the angular position of first order maximum is given as

`a sin\theta = (3)/(2)\lambda`

so we will have

`\theta = (27)/(2)`

`\theta = 13.5 degree`

so we have

`a = (3\lambda)/(2sin\theta)`

`a = (3(534 nm))/(2 sin13.5)`

`a = 3.43 * 10^(-6) m`

So the grating space is given as

`a = 3.43 * 10^(-6) m`