Would you -- drawing of wood blocks and a ruler to measure a lens

[Syndy]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown. Also, thread title edited to make it more descriptive. >[/color]

The question is asking me to draw a diagram to show how, in the laboratory you would use two rectangular blocks of wood and a metre rule to measure the thickness of a lens as accurately as possible.

I don't know how to draw it. Where to put the blocks and the lens!

 

[phinds]

The question is asking me to draw a diagram to show how, in the laboratory you would use two rectangular blocks of wood and a metre rule to measure the thickness of a lens as accurately as possible.

I don't know how to draw it. Where to put the blocks and the lens!

Do you understand trigonometry, or for that matter just similar triangles ? Have you taken algebra?

Just FYI it's a bad idea to use such an non-specific subject thread, and it's a good idea to give some sense of what you know in addition to what you are trying to find out. That is, where are you in school? What level class is this for?

Someone might give you an excellent answer using trig only to find out that you don't know any trig.

 

[Syndy]

The question has nothing to do with trigonometry. The question is in alternative to practical past paper physics exams of IGCSE.

There is no other information in the question for me to use trigonometry.

Sorry if I posted it in the wrong thread, just unintentional mistake!

 

[phinds]

So, I ask again: Do you understand similar triangles ? Have you taken algebra?

 

[Syndy]

Yes. I understand it. I study maths this year.

 

[phinds]

Yes. I understand it. I study maths this year.

OK, think of a way you could make similar triangles with enough known about various sides to get you what you want to know

 

[haruspex]

Seems to me you'll need to make some assumptions about the relative dimensions of lens and wood blocks. It doesn't give any hints on that?
Also, with the method I'm thinking of, a bit of trig will help to get a more accurate answer.

 

[Syndy]

Ok. Thank you very much for trying to help me. I appreciate it.

 

[phinds]

Seems to me you'll need to make some assumptions about the relative dimensions of lens and wood blocks. It doesn't give any hints on that?
Also, with the method I'm thinking of, a bit of trig will help to get a more accurate answer.

Uh ... that's what the meter stick is for, and no, it doesn't require trig just geometry and algebra

 

[DaveC426913]

Unless these blocks of wood are planks, I am not sure how you'd do this.

 

[phinds]

Here's what I'm thinking. I DID unwittingly make the unwarranted assumption that the lens is convex. If it's concave this doesn't work. Inaccuracies will be involved in making sure your line of sight is the exact center of one surface of the lens and that you are measuring to the exact place where the other side of the lens hits the table. The block on the right will have to be off to the side of the lens (line of sight is blocked/distorted by the lens AND the bottom of the block may need to be so close it would be blocked by the lens) and you get another inaccuracy in lining up the bottom of that block with the line of sight through the center of the top side of the lens. It's all a bit messy but seem to me it would work. All the "Mx" things are measured. M1 might be the full height of the meter stick but it doesn't have to be. I am of course assuming that "meter stick" means a measuring stick because it's the only measuring thing you have so if it's just a stick one meter long you are dead in the water. M2 isn't used but that block is needed for lining things up.

Haruspex, this is a bit different than what I said in the PM

 

[haruspex]

Here's what I'm thinking. I DID unwittingly make the unwarranted assumption that the lens is convex. If it's concave this doesn't work. Inaccuracies will be involved in making sure your line of sight is the exact center of one surface of the lens and that you are measuring to the exact place where the other side of the lens hits the table. The block on the right will have to be off to the side of the lens (line of sight is blocked/distorted by the lens AND the bottom of the block may need to be so close it would be blocked by the lens) and you get another inaccuracy in lining up the bottom of that block with the line of sight through the center of the top side of the lens. It's all a bit messy but seem to me it would work. All the "Mx" things are measured. M1 might be the full height of the meter stick but it doesn't have to be. I am of course assuming that "meter stick" means a measuring stick because it's the only measuring thing you have so if it's just a stick one meter long you are dead in the water. M2 isn't used but that block is needed for lining things up.

Haruspex, this is a bit different than what I said in the PM

View attachment 78949

I can see a few difficulties.
First, I assumed you could not see through the lens like that, so all lines related to the lens would be tangents. That's one place where a bit of trig can improve the precision.
Second, there's nothing given about flat ground to place the blocks on. It might be hard to arrange that intended right angles are such, so again some trig may be needed. To that end, it might be better to lay the right hand block down and place the lens on it. You can still use the distal end of the block for the line of sight, and using the metre rule you can project the surface of the right hand block to mark off where this base line meets the upright of the left hand block.
(Btw, why not M2/(M4+M5)?)

 

[phinds]

Yes, M2/ (M4+M5) works equally well. I did make the assumption that you have a lab table, since the problem says it's to be done in a lab. That does not seem even remotely far fetched to me. I already specifically explained how you avoid the issue of the lens getting in the way. I don't get what you mean about the lines being tangents.

 

[haruspex]

Yes, M2/ (M4+M5) works equally well. I did make the assumption that you have a lab table, since the problem says it's to be done in a lab. That does not seem even remotely far fetched to me. I already specifically explained how you avoid the issue of the lens getting in the way. I don't get what you mean about the lines being tangents.

I don't believe it will be possible to see through the lens at such a shallow angle, certainly not without considerable distortion. Simpler to treat the lens as opaque and work with tangents.

 

[DaveC426913]

I have wondered: why a lens? Why not a billiard ball or a coin?

And yes, if a lens, surely its shape is important to know.