# Sun spectroscopy - Home experiment

We let the sun light run through a 5x3x3cm triangular glass prism and we examined the formed 'rainbow' in search of Fraunhofer lines. However, even though we looked close enough (even with a magnifying glass), we were unable to see any Fraunhofer lines and the spectrum appeared perfectly continuous.

I am attaching a few pictures of the experiment. Two A4 format blank papers were positioned sort of diagonally, as to make a diagonal cross-section of the spectrum, so that it could be apparently stretched as wide as possible.

What are we doing wrong? Why can't we see any Fraunhofer lines in the pictures?

• The Fraunhofer lines are quite narrow. You must make sure the effective aperture of the setting is large enough for the lines to not vanish due to diffraction and that the projected spectrum is focussed accurately enough. – Count Iblis Mar 6 '15 at 17:25

The resolving power of a prism is given by the formula $$\frac{\lambda}{\Delta \lambda} = b\ \frac{dn}{d\lambda},$$ where $b$ is the base length of the prism, $\lambda$ is the wavelength and $n(\lambda)$ is the refractive index.

You don't say, but let's assume you are using a crown glass prism. According to this useful document, crown class has $dn/d\lambda \simeq 400$ cm$^{-1}$ in the yellow part of the spectrum. So, for a prism of baselength $b=5$ cm, you have a resolving power of about 2000 and hence in the yellow part of the spectrum you should be able to resolve lines with a separation of 0.25 nm. This should easily be sufficient to see H$\alpha$, the sodium D lines etc.

You have not said how you are focusing the light? I suspect what you are doing wrong is you have not built yourself a spectrograph; something like the image below (from here). You need to focus the dispersed light and you also need to make sure you have a slit-like aperture for best results.

If you don't do something like this, then effectively what you have are heavily overlapping images of the face of the prism at each wavelength. The overlap is likely to be so large that it destroys your resolving power. A lens can focus these images so that light of a particular wavelength falls at one spot on your screen.

EDIT: As a thought experiment, consider putting a filter in front of the prism that only lets red light at a particular wavelength through. What will the projected image look like in your current setup? My guess is that it will look like a red rectangle, with a width that is proportional to the size of the prism face that the light exits from.

Now change the central wavelength of the filter by 1 nm. The position of the projected rectangle will change slightly, but not by anywhere near the width of the rectangle, so that its image would overlap almost totally with the previous image. i.e. Light separated by only 1 nm is smeared together and cannot be resolved.

What you need to do with the lens is focus the rectangle down so that ideally it is just a very narrow slit-like image. That way a change in wavelength of 1nm will produce a clearly separated image.

• "All blue light" at the top border in the image should read "All red light". – Jens Mar 6 '15 at 19:49
• @Rob Jeffries We didn't use a slit; the sun illuminated the entire prism. Likewise, we didn't use a focusing lense either. How wide, do you think, should the slit be? (The prism is 5x3x3cm). Would a magnifying glass (7cm in diameter) be good enough for focusing the light? – Roll Mar 6 '15 at 22:22
• @Roll Give it a go. I think you can do without a slit. You'll need a lens significantly bigger than the prism to get a decent focus if it is fully illuminated. – Rob Jeffries Mar 6 '15 at 22:42
• @Rob Jeffries Also, I don't quite understand why I need the focusing lens in the first place; the rainbow image I see is not out of focus, not blurred or anything. Or is it used just to magnify the image? Using a focusing lens, should I see the whole spectrum, or just one or two colours? – Roll Mar 6 '15 at 22:48
• @Roll How's that? The focusing lens will make the image smaller, but you should then see the Fraunhofer lines. You will have to play with the focus. An idea would be to try illuminating the prism from a distance with a fluorescent lamp, as this would have some sharp spectral (emission) lines that you could get into focus. For a given separation of prism and magnifying lens, that will tell you how far away your screen needs to be from the lens. – Rob Jeffries Mar 6 '15 at 23:28

I was unable to see any Fraunhofer lines with the sun light, despite using a focusing lens. However, I tried examining the light of a fluorescent bulb instead. I didn't manage to project the image on a sheet of paper, but I was able to take a direct picture of the image in the prism. The result is a bit more satisfying:

/

Are these four lines a representation of the the mercury element in the bulb?

• You seem to be on your way, but it looks to me like either your focus is not very good or you need a narrower slit if you are going to be able to see the Fraunhofer lines. – dmckee Mar 8 '15 at 17:32