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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?

Respuesta :

Answer:

the grating space is given as

[tex]a = 3.43 \times 10^{-6} m[/tex]

Explanation:

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

[tex]a sin\theta = \frac{3}{2}\lambda[/tex]

so we will have

[tex]\theta = \frac{27}{2}[/tex]

[tex]\theta = 13.5 degree[/tex]

so we have

[tex]a = \frac{3\lambda}{2sin\theta}[/tex]

[tex]a = \frac{3(534 nm)}{2 sin13.5}[/tex]

[tex]a = 3.43 \times 10^{-6} m[/tex]

So the grating space is given as

[tex]a = 3.43 \times 10^{-6} m[/tex]

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