Diffraction Grating Questions

[spoonthrower]

I just want to make sure i got these questions answered correctly about multiple slit diffraction gratings: specifically a grating spectroscope.

1. Why is the 2nd order spectrum more "spread out" than the first order spectrum?

Is it because one light wave has to travel 2 wavelengths farther than the other wave of light? Also because the angle increases as you move from the first order to the second order spectrum?

2. Explain why it is important to illuminate as much of the grating as possible.

Is it because you need as much light as possible to produce mth order maximums. If there is not enough light then some maximums won't show up.

Please help with anything i left out, should add, or did wrong. thanks.

 

[Astronuc]

Is it because one light wave has to travel 2 wavelengths farther than the other wave of light? Also because the angle increases as you move from the first order to the second order spectrum?

Are you asking or stating an answer?

Take a point some distance 'a' from a plane. A beam of light is pointing normal to the plane. Then rotate the beam of light some angle. What happens to the distance between the point when the light was shining normal (directly at) the plane, and the point when the light shines at angle. Remember the beam of light is on the hypotenuse of a triangle formed by the normal between point and plane, and the distance from normal to the light as it strikes the plane at an angle, and the beam itself.

Hopefully that's not too confusing.

The diffraction pattern will certainly be brighter with a more intense light, but "as much of the grating as possible" seems to indicate illuminating as many slits as possible. What would be the consequence of that? In other words, if one illuminates 2, 3, 4, 5, 6, . . . slits, what happens?

 

[kyle8921]

I would like to confirm that your answers to the two questions are correct. The second order spectrum is more spread out because the light waves have to travel a longer path difference compared to the first order spectrum. This results in a larger angular separation between the two waves, leading to a wider spectrum.

It is important to illuminate as much of the grating as possible because the diffraction pattern from a grating is dependent on the number of slits illuminated. The more slits that are illuminated, the more diffraction maxima will be produced, resulting in a clearer and more accurate spectrum. Additionally, if only a small portion of the grating is illuminated, the intensity of the diffracted light will be lower, making it difficult to detect the higher order maxima.

Overall, your answers are correct and provide a good understanding of the principles behind diffraction gratings. If you would like to enhance your understanding, you may also want to consider the concept of coherence length and its effect on diffraction patterns, as well as the relationship between the number of slits and the grating spacing. Keep up the good work!