Diffraction grating and red light

[Kris1120]

Homework Statement

White light is spread out into its spectral
components by a diffraction grating.
If the grating has 2469 lines/cm, at what
angle does red light of wavelength 635 nm
appear in first order?
Answer in units of ◦.

Homework Equations

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

The Attempt at a Solution

theta = inverse sin [( 1 * 635 e-9 m) / 24.69 m} = 1.4735 e -6 degrees

 

[alphysicist]

Hi Kris1120,

Homework Statement

White light is spread out into its spectral
components by a diffraction grating.
If the grating has 2469 lines/cm, at what
angle does red light of wavelength 635 nm
appear in first order?
Answer in units of ◦.

Homework Equations

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

The Attempt at a Solution

theta = inverse sin [( 1 * 635 e-9 m) / 24.69 m} = 1.4735 e -6 degrees

In your formula, d is the distance between grating lines. If there are 2469 lines in every cm, what is the distance between each line?

 

[Kris1120]

I see... its 1 / 2469 cm! Thank you!

 

[alphysicist]

I see... its 1 / 2469 cm! Thank you!

That's right (as long as you meant (1/2469) cm; some people inadverdently put the cm in the denominator for this type of problem).

Glad to help!