Question

If sunlight shines straight onto a peacock feather, the feather appears bright blue when viewed from${15}^{\circ }$on either side of the incident beam of light. The blue color is due to diffraction from parallel rods of melanin in the feather barbules, as was shown in the photograph on page $940$. Other wavelengths in the incident light are diffracted at different angles, leaving only the blue light to be seen. The average wavelength of blue light is $470nm$. Assuming this to be the first-order diffraction, what is the spacing of the melanin rods in the feather?

Short answer

The feather's melanin rods are $d=1.82\mu m$inches apart.

Step-by-step solution

Step: 1 Wavelength of blue light:

High energy visible ($HEV$) light, often called blue light, has the shortest wavelength of actinic ray (role="math" localid="1649157295025" $380nm$ to $500nm$) so produces the foremost energy.

Step: 2 Derivating part:

The grating spacing as

$$\begin{gathered} d\sin \left({\theta }_m\right)=m\lambda \\ d=\frac{m\lambda }{\sin \left({\theta }_m\right)}. \end{gathered}$$

Step: 3 Finding spacing:

The spacing as

$$\begin{gathered} d=\frac{1\times 4.7\times {10}^{-7}}{\sin \left({15}^{\circ }\right)} \\ d=1.82\times {10}^{-6}\mathrm{m}. \end{gathered}$$