Radius of curvature experiment

[lynsey]

Hi there

In an experiment I have calculated the radius of curvature for a +0.25D lens using Newtons rings and have obtained a value for 892mm, but the radius of curvature for a +0.25D lens is just over 2 metres. why is the value i got so much lower? do i have to double the value i got for the radius to take into account the 2 surfaces of the lens or not? please help I am really stuck!

thanks for any help!

 

[Redbelly98]

Can you show the equations you used, and how you calculated your answer?

 

[lynsey]

the equation we were given to use was

r = d(squared) / 4.N.wavelength

the wavelength was 0.000588m
the value for d(squared) was 1.955

My actual value was 831mm (sorry wrote the wrong figure down before)

although i think there may be a problem with the equation we were given to use as I have found another one:

The radius of the Nth Newton's bright ring is given by :

rn = [(N-1/2). wavelength. R]1/2

hope that makes sense to you:s its the one from wikipedia
http://en.wikipedia.org/wiki/Newtons_rings

i measured the dark rings...so you can ignore the -1/2 and just use N

this seems to give me a figure of 3000 odd, which gives a power of 0.15D, which when doubled then gives 0.30D...i know it is 0.05D out but this may be due to experimental error?

how does that sound or is the equation we were given to use the correct one?

thanks for any help you can give me! :)

 

[Redbelly98]

By the way, welcome to PF.

the equation we were given to use was

r = d(squared) / 4.N.wavelength

That's right, since this is for dark fringes. Do you know what each term in that equation is? Since there are 2 different radii or diameters represented here, it is important to keep track of which is which. I.e., r is not simply "the radius", it is "the radius of ____?".

And similarly for "d".

the wavelength was 0.000588m
the value for d(squared) was 1.955

Let me suggest here that you get in the habit of being careful about writing units correctly. It appears that you are using mm for length units. Do you see what is wrong with BOTH of the values you have written above? (Hint: it has something to do with units.)

My actual value was 831mm (sorry wrote the wrong figure down before)

Looks correct given your values, assuming that N=1 (is it?)

Here is a question for you: how are you measuring the fringe diameter? It must be about 1.4 mm, to get the d²=1.955mm² value you reported. It is difficult to measure it that accurately without some kind of precision instrument.

although i think there may be a problem with the equation we were given to use as I have found another one:

The radius of the Nth Newton's bright ring is given by :

rn = [(N-1/2). wavelength. R]1/2

hope that makes sense to you:s its the one from wikipedia
http://en.wikipedia.org/wiki/Newtons_rings

i measured the dark rings...so you can ignore the -1/2 and just use N

I agree, ignore the "-1/2" for the dark rings. Then you get

r_N = [N . wavelength . R]^1/2

If you solve this equation for "R", you get essentially the same equation you had earlier.

Basically, I've given you a list of things to think about more:

• Define the terms in your first equation (see above).
• What are the values for wavelength and d², with correct units?
• Is N equal to 1?
• How was the fringe diameter measured?
• Solve the Wikipedia equation in terms of "R". Ignore the "-1/2", but do not ignore the "1/2" exponent. You should get your original equation, or something equivalent.

p.s. feel free to use ^2 or ^(1/2) for writing exponents in equations.