Physics youngslits question.

The light from a `special LED' consists of two colours of light with wavelengths of 530nm and 630nm respectively. The light is shone through a diffraction grating with 500lines/mm, and the two colours need to be separated by at least 5.0∘. What is the minimum order of interference needed in order to do this?

How do I do this one?

Reply 1

phys981

10

For the diffraction grating (not youngs slits) you ahve an equation

nλ = d sin theta

The n has to be the same for both, d is the diffraction grating spacing and you have two wavelengths.

At the moment I can't see any other way to do it that start from n=1 (n=0 will give angle zero for both) and solve for theta until you find 5º of difference for the two wavelengths. (ie, start with n=1 and if the difference isn't enough, try n=2 and so on)

Someone else more inspired might come up with a shortcut.

Original post by joyoustele

The light from a `special LED' consists of two colours of light with wavelengths of 530nm and 630nm respectively. The light is shone through a diffraction grating with 500lines/mm, and the two colours need to be separated by at least 5.0∘. What is the minimum order of interference needed in order to do this?
How do I do this one?

Original post by phys981

For the diffraction grating (not youngs slits) you have an equation

nλ = d sin θ

The n has to be the same for both, d is the diffraction grating spacing and you have two wavelengths.

At the moment I can't see any other way to do it that start from n=1 (n=0 will give angle zero for both) and solve for theta until you find 5º of difference for the two wavelengths. (ie, start with n=1 and if the difference isn't enough, try n=2 and so on)

Someone else more inspired might come up with a shortcut.

I would not say the following is a shortcut but some learning moments for the students after they have successfully answered the question.

For such question, I would usually have some extension questions or discussions depending on the level of students.

If this is the first time that the students are attempting such question, I would get them to use the brute force method outlined by phys981.

Then I would have a discussion using a spreadsheet calculation based on the brute force method or guiding questions to explore for a “shortcut”.

Let θ_Sn and θ_Ln be the angles for the wavelength of 530nm and 630nm respectively based on the diffraction grating formula (d sin θ = nλ)

Compute the ratio λ /d for the wavelength of 530nm and 630nm respectively and then find the difference (which is 0.05).

Using the brute force method, the following can be “deduced” for "small angle":

\theta_{Ln} - \theta_{Sn} \approx \dfrac{n \lambda_{Ln}}{d} - \dfrac{n \lambda_{Sn}}{d}

Note that the angle in radians NOT degree.

So for 5°, convert it to radian which is about 0.087 rad. Substitute 0.087 rad to the above approximated equation to solve for n.

Spoiler

Reply 3

joyoustele

OP

19

Original post by Eimmanuel

I would not say the following is a shortcut but some learning moments for the students after they have successfully answered the question.

For such question, I would usually have some extension questions or discussions depending on the level of students.

If this is the first time that the students are attempting such question, I would get them to use the brute force method outlined by phys981.

Then I would have a discussion using a spreadsheet calculation based on the brute force method or guiding questions to explore for a “shortcut”.

Let θ_Sn and θ_Ln be the angles for the wavelength of 530nm and 630nm respectively based on the diffraction grating formula (d sin θ = nλ)

Compute the ratio λ /d for the wavelength of 530nm and 630nm respectively and then find the difference (which is 0.05).

Using the brute force method, the following can be “deduced” for "small angle":

\theta_{Ln} - \theta_{Sn} \approx \dfrac{n \lambda_{Ln}}{d} - \dfrac{n \lambda_{Sn}}{d}

Note that the angle in radians NOT degree.

So for 5°, convert it to radian which is about 0.087 rad. Substitute 0.087 rad to the above approximated equation to solve for n.

Spoiler

I just didnt understand the question well. Thanks a lot, Very much appreciate it.