Accurately Reading a Vernier Scale

[Kazza_765]

During a physics prac today, we were using a traveling microscope with a vernier scale. My demonstrator told me I was reading the scale wrong, and as much as I tried to convince him otherwise he insisted he was right. Can anyone here tell me what the correct value to be read from the vernier scale pictured below is. The lower set of lines is a section of the centimetre scale, the top is the vernier scale. Assume that the '0' line on the vernier scale is just slightly to the right of the line highlighted in blue, and that the two lines marked in red line up perfectly. I read this as being 3.112cm but he said that was wrong and I could only be accurate to 0.01cm (even though he couldn't give me a correct reading).

 

[krab]

looks like 31.25mm to me.

 

[Kazza_765]

I'm curious how you got 31.25mm. 31mm I understand, but I thought next you look for where the two scales line up and take the value from the top scale. So in this case we get 31mm + 0.12 mm = 31.12mm.

Ps. I realize that in this diagram the scales line up in several places, which is why I highlighted one of the lines in red, but it was the best I could do with powerpoint.

 

[FredGarvin]

I agree with your 31.12 (or 31.21 but I know your diagram is off). I would make sure to double check the smallest increments on the vernier though. If it is on the order of .01 mm and not .01 cm then I say you are correct.

 

[krab]

Imagine the upper scale is moved just a tiny bit so that the first line lines up with 31mm on the bottom. This would obviously be 31.00mm. At the same time, the line labelled .1 will line up with the 4 (cm). This is how a vernier works; the 10 lines on the upper scale fall on 9 lines on the lower. This shows that the lines beyond .1 on the upper scale are superfluous. Now imagine moving the upper scale slowly back towards the way it was in the picture. First the next-to-leftmost line will line up with the 32mm line; that would be 31.1mm: then the next line lines up; thatr would be 31.2mm: a little more, and both the 3rd and 4th are eqally aligned, as is the case in the picture; that's 31.25mm. Imagine you move it further: as soon as the 10th line lines up (meaning 31 + 1.0 = 32.0mm), you notice also that the first line lines up with the 32mm on the bottom scale. This consistency is what you look for in determining how to interpret the scale.

 

[Kazza_765]

Yeah I think that is what my demonstrator was getting at because that is what the example in our book looked like. However, the vernier scale we were using didn't have 10 lines in 9, it had 49 lines in 50 (equivalent to 99 lines in 100 on my diagram but we had 0.5cm divisions on the lower scale). And with 49 lines in 50 it had to be read with an attached magnifying glass. So if I started with the first line at the 31mm mark, and slowly moved it to the 31.5 mm mark, first the 0.01mm mark at the top would line up perfectly, then the 0.02mm mark etc.. all the way to 0.49 mm.