Question

What is most likely the color of the light whose second-order bright band forms an angle of 13.5° if the diffraction grating has 175 lines per mm?

Answer 1

the answer is red, just has that question

Answer 2

Answer : The color of light is red.

Explanation :

Given that,

Numbers of lines in a diffraction grating, n = 175 lines per mm

The grating equation for the bright band is given by :

d sinФ = n λ

Where,

d is the distance between the slits

Ф is the angle to maxima

n is the order, n = 2

λ is the wavelength of the light.

Since, d = 1/N

N is the numbers of lines

So,
`(1)/(N)sin\phi=n\lambda`

`\lambda=(sin\phi)/(Nn)`

converting mm to m

`\lambda=(sin (13.5))/(175000\ m* 2)`

λ = 6.66 × 10⁻⁷ m

or

λ = 667 nm

This shows the wavelength of red light. So, the color of light emitted will be red.

Hence, this is the required solution.