How Is the Diffraction Angle Calculated for Different Wavelengths?

[MarcL]

Homework Statement

A grating places a spectral line of wavelength 681 nm at 12 degrees in first order. At what angle is a line of wavelength 439 nm observed in second order?

Homework Equations

I believe dsinθ= mλ

The Attempt at a Solution

This is where I get lost, I can solve for every problem in difraction ( We did Rayleigh's criterion, double slit / single slit difraction) but I can't seem to be able to start a problem that involves grating, any pointers on how to start would be nice ^^ I just want to know how to approach the problem! :)

 

[TSny]

As far as finding the angles for the bright fringes, there is no difference between a grating and a double slit.

One approach to this problem would be to use the information about the 681 nm line to determine the distance d between two slits in the grating.

 

[MarcL]

Ah, it worked. Thanks a lot ^^ Just a little question, if you don't mind answering it of course. If ever it asked me to look for the distance between the two waves, would I need to compare the equations or something?

 

[TSny]

Ah, it worked.

Good!

If ever it asked me to look for the distance between the two waves, would I need to compare the equations or something?

I'm not sure what you mean by "distance between the two waves". Can you clarify that?

 

[Nickie]

I would approach this problem by first understanding the concept of diffraction gratings and how they work. A diffraction grating is a device that consists of a series of equally spaced parallel slits or lines that can diffract light into its component wavelengths. The equation you have mentioned, dsinθ= mλ, is known as the grating equation, where d is the distance between the slits, θ is the angle at which the light is diffracted, m is the order of the diffraction, and λ is the wavelength of the light.

In this problem, we are given the wavelength and angle for the first order diffraction, which can be written as dsinθ = 681 nm. We can rearrange this equation to solve for d, which would be the distance between the slits. Once we have the value of d, we can then use the same equation to solve for the angle at which the second order diffraction of 439 nm would occur.

Another approach could be to use the relationship between the wavelengths and the angles of diffraction. As the wavelength decreases, the angle of diffraction also decreases. This relationship can be described by the equation λ = dsinθ. Knowing this, we can set up a ratio between the first and second order diffraction angles and solve for the unknown angle.

In summary, to solve this problem, we need to use the grating equation, understand the relationship between wavelength and angle, and set up a ratio between the known and unknown angles. I hope this helps in approaching this problem.