Parabola Question (1 Viewer)

[rand_althor]

Saw this question in an exam paper but unfortunately there were no answers. Could someone please assist?

In the Michaelson and Morley experiment the pair was attempting to prove the existence of the luminiferous aether by setting up the equipment as show below.

Mistakenly, they used a concave mirror instead of a half silver mirror as the coherent light source travels in a straight line from the base source to the concave mirror and is reflected onto a focal point F.

The mirror lies on the Cartesian plane. By assuming the principle axis of the mirror is aligned with the y axis in the Cartesian plane, find the focus point.

 

[VBN2470]

Not sure about this, but is it ?

 

[rand_althor]

Unfortunately I do not have answers. How did you get that answer?

BTW the paper is SSC Blackwattle Bay Campus 2011 Higher School Certificate Assessment Task 1. If someone has answers to that, please do share the solution.

 

[VBN2470]

I could be completely wrong, but I simply considered the latus rectum of the parabola (which I assumed was 10). The latus rectum of a parabola is the line segment through the focus perpendicular to the major axis (which has both endpoints on the curve). The length of this latus rectum is given by 4a, where a is the focal length. Thus solving for a in 4a = 10, you will find that the point of focus is .

 

[rand_althor]

Doesn't the latus rectum pass through the focus though? If the diagram is to scale, it doesn't seem like a line that passes through the focus and is perpendicular to the major axis could have a length of 10 units.

 

[VBN2470]

I know what you mean, but with the given information, I am not able to see anything else. Don't know whether it is to scale or not but it's the closest thing I can think of. As I said, I could be completely wrong.

 

[rand_althor]

Okay fair enough. There could be something missing from the picture as that was the case for another question in the file.

Thanks for the help!

 

[InteGrand]

We're not even told the mirror is parabolic, are we? There's no reason that it has to be; it could be spherical theoretically (although this would suffer from spherical aberration, but spherical ones are common for concave mirrors). And this type of question (optics) seems more in the realms of Physics.

 

[InteGrand]

This problem as posed doesn't appear to have enough information to solve. We don't seem to be told what the 10 cm represents (and it doesn't look like the latus rectum of a parabola, since the ends of the mirror described by the "10 cm" don't appear to come anywhere near the focus; they should have been in line with it if it were the latus rectum).

 

[rand_althor]

I suppose the question is dodgy or the file has been changed in some way.