Why are there two vernier scales on a prism spectrometer and why are they 180 degrees apart?
Example image (source):
I have some idea that it reduces the error in measurements but I don't exactly know how it does that.
this article reasons as follows:
"Record both VERNIER readings (in minutes). Average the two vernier readings (to eliminate any systematic error from misalignment of the circle scale with respect to bearing axis), and add the result to one of the angle scale readings."
can someone elaborate this reasoning for me ?
Best Answer
As pointed out in the comments, the short answer to your question is: To minimize or counter the errors produced in the case when the axis of rotation of telescope and prism table/vernier table do not coincide.
Long Explanation: Assume that the point $O$ in the given figure represents the center of the prism/vernier table of the spectrometer, through which the axis of rotation passes. And assume that the point $O'$ represents the point of intersection of the axis of rotation of the telescope and the plane of the table. Ideally, $O$ and $O'$ should coincide but say, due to some fault in the bearings they displace a little.
In the ideal case, when $O$ and $O'$ do coincide, angle $\theta$ is subtended by $O$ or $O'$ on either of vernier scales ($V_1$ or $V_2$) is equal and thus only one vernier scale will be enough to the job.
In case the two points of rotation displace apart i.e. do not coincide with each other, $O$ (point of rotation for vernier table) will still subtend equal angle $\theta$ on both vernier scales but $O'$ (point of rotation for the telescope) will not because $\alpha$ and $\beta$ will differ and this introduces an error in the readings. To counter the error introduced by displacement of points of rotation, we take the mean of both the angles $\alpha$ and $\beta$ and thus we use two verniers instead of just one.
EDIT: In the case when $O$ and $O'$ coincide the angles differ by 180° but when they do not coincide, $\alpha$ and $\beta$ do not differ by 180°.