Chapter 36: Q44P (page 1112)

Perhaps to confuse a predator, some tropical gyrinid beetles (whirligig beetles) are coloured by optical interference that is due 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 26⁰ in light with a wavelength of 550 nm. What is the grating spacing of the beetle?

Expert verified

$2.44 \times 10^{- 6} m$

Step by step solution

The given data is listed below as:

The condition for maxima of the diffraction grating is:

$d s i n θ = m λ$

Here, d is the distance between adjacent rulings and $λ$ is the wavelength of light.

The condition for maxima of the diffraction grating is:

$d \sin (θ) = m λ$

Where, $m = 0, \pm 1, \pm 2, . . . .$ and $θ$ is the angle between the central axis and the corresponding point.

Now, the angle between the first maxima and central axis is,

$θ = \frac{26 °}{2} = 13 °$

Therefore, the grating spacing of the beetle is calculated using the equation:

$d \sin (θ) = m λ d = \frac{m λ}{\sin θ}$

For $m = 1$ , the above expression can be calculated as:

$d = \frac{(1) (550 \times 10^{- 9} m)}{\sin (13 °)} = 2.44 \times 10^{- 6} m$

Thus,the required grating spacing of the beetle is $2.44 \times 10^{- 6} m$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.