Question

Structures on a bird feather act like a diffraction grating having 8000 8000 lines per centimeter. What is the angle of the first-order maximum for 452 nm 452 nm light shone through a feather?

Answer 1

Answer:

Angle of first order maximum, $\theta=21.19^{\circ}$

Explanation:

Given that,

Wavelength of the light, $\lambda=452\ nm=452\times 10^{-9}\ m$

Number of lines, N = 8000 per cm

The relation between the number of lines and the slit width is given by :

$d=\dfrac{1}{N}$

$d=\dfrac{1}{8000/cm}$  

$d=0.000125\ cm=1.25\times 10^{-6}\ m$

The equation of grating is given by :

$d\ sin\theta=n\lambda$

n = 1

$sin\theta=\dfrac{\lambda}{d}$

$sin\theta=\dfrac{452\times 10^{-9}}{1.25\times 10^{-6}}$

$\theta=21.19^{\circ}$

So, the angle of the first-order maximum is 21.19 degrees. Hence, this is the required solution.