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

Angle of first order maximum,
`\theta=21.19^(\circ)`

Step-by-step explanation:

Given that,

Wavelength of the light,
`\lambda=452\ nm=452* 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=(1)/(N)`

`d=(1)/(8000/cm)`

`d=0.000125\ cm=1.25* 10^(-6)\ m`

The equation of grating is given by :

`d\ sin\theta=n\lambda`

n = 1

`sin\theta=(\lambda)/(d)`

`sin\theta=(452* 10^(-9))/(1.25* 10^(-6))`

`\theta=21.19^(\circ)`

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