Why and How of the schuster's method.

[x3qt0r]

We have often used schuster's method while performing any experiment on spectrometer.
But I am not able to get the logic behind it.
how does the turning of prism helps in focusing of collimator and telescope for "parrallel light"


let me give the schusters method in brief:

Focus the eye piece of the telescope on the cross wires and do not disturb this adjustment here after.Illuminate the slit of the collimator with sodium light.Adjust the width of the slit so that it is as narrow as possible.Place the prism on the table at its center with its refracting edge vertical and grounded face roughly parallel to the length of the collimator.The prism table is slowly rotated until the refracted image of the slit is in the minimum deviation position.
Rotate the prism table slowly so that the refracting edge of the prism of refracting angle "A" moves towards the telescope so that the telescope receives the refracted rays at an angle greater than the angle of minimum deviation for the ray.The telescope is then focused to make the image of the slit sharp.
The prism table is now rotated so that the refracting angle of the prism moves towards the collimator.The collimator is now adjusted to make the the image of the slit very sharp.
The above two steps are continued until the image of the slit is sharp and without parallax with the vertical cross wire.

does this thing has anything to do with the fact that at minimum deviation the light rays inside the prism are parallel to the prism base?

 

[Debajyoti Sengupta]

Here's how you can make sense of this method.
Consider the deviation vs incidence plot you obtained from experiment(delta-i). You would notice the plot has a minimum at a particular angle of incidence. You begin your adjustment by reaching this angle of incidence (by proper adjustment of prism and telescope). In this setup, the deviation is minimum. Another way of saying that is that image and object are equidistant from the point of observation (your eye). When you move the telescope away from the direct ray, you are now, not looking at the image formed. Thus you turn the prism table to re-obtain the image. Whilst doing so, what you effectively did was either reduce or increase the angle of incidence (turning the prism or prism table would definitely increase or decrease angle of incidence). And in doing so, you effectively changed the position of image. Image comes closer if deviation is large (spectral line is thick, not sharp); Image goes far if deviation is less (spectral line sharp).

Now look at you delta-i plot. You would notice the plot isn't symmetric about minimum deviation point. (If it is, then your 'fitting' is wrong!) It is more steep for incident angles less than I am (angle of incidence for which deviation is minimum).

This asymmetrical nature is what makes Schuster's method work. If you increase the angle of incidence, ie, move to the right of im, you would notice for small change in i change in delta is small. If you decrease the angle of incidence, ie move to the left of im, for small changes in i changes in delta would be larger than the previous case.

Go back to the first paragraph. You now know that sharper image means less deviation angle which means you are on the right end of im. This is called slanting position (could be wrong, don't quote me on this). Your image is far off than point where you had focused your telescope Adjust your telescope to get sharp line.

Change i (rotate prism table), you would now see the line is thicker and blurry possibly. That means deviation is large and image is nearer than the point your telescope was focused on. Since your objective is to adjust both collimator and telescope for parallel rays you should now adjust your collimator t get sharper line (your telescope is already adjusted for a far off point, meaning parallel rays). BTW this position is called normal position (again don't quote me)

Keep repeating these steps until you get sharp lines for both normal and slanting positions. Once you get that you can claim you have adjusted your telescope and collimator for parallel rays (ie focused on a far off point)

Hope this helps!