Calculate Radius of Curvature for Newton's Rings - 5th & 15th Bright Ring

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In summary, to calculate the radius of curvature for the 5th and 15th bright rings formed by sodium light with a wavelength of 589.3nm, we will need to use the formula for the radius of a circle and the distance between the center of the rings and the center of the circle. This can be found by using the formula for constructive interference and then using the Pythagorean theorem to calculate the radius. Finally, we can take the average of the two calculated radii to get a more accurate estimation of the radius of curvature.
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The-Exiled
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Homework Statement


The diameter of the 5th and 15th bright ring formed by sodium light (wavelength = 589.3nm) are 2.303mm and 4.134mm respectively. Calculate the radius of curvature.

Homework Equations



DON'T ASSUME THAT THE RINGS ARE PERFECTLY CENTRED
(I assume that means that the radius of the rings can't be obtained by simply dividing the diameter by 2)

The Attempt at a Solution


I am not sure how to start finding the radius of the rings or if I need it at all? I know there is a [tex]\pi[/tex] phase change and hence the constructive interference is when
2 x [distance in air] = (m + 0.5)[tex]\lambda[/tex].

I've tried finding the ratios of diameters for some reason, just to see if it lead to anything... It didn't... Can anyone help me please?

Thank you very much
 
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  • #2
for your question. It's great to see that you are thinking critically about the problem and considering the possibility that the rings may not be perfectly centered. In order to calculate the radius of curvature, we will need to use the formula for the radius of a circle, which is r = d/2, where r is the radius and d is the diameter. However, since we cannot assume that the rings are perfectly centered, we will need to use the distance between the center of the rings and the center of the circle, which we will call x.

Using the formula you mentioned for constructive interference, 2x = (m + 0.5)λ, we can solve for x by plugging in the known values for the wavelength and the order of the ring (m). Once we have the value for x, we can use the Pythagorean theorem to calculate the radius of the circle, which is given by the equation r = √(x^2 + (d/2)^2).

In this case, we will need to calculate the radius for both the 5th and 15th ring, using the respective diameters given. Once we have the two values for the radius, we can use them to calculate the radius of curvature by taking the average of the two values. This will give us a more accurate estimate, taking into account any potential errors in the measurement of the ring diameters.

I hope this helps and good luck with your calculations!
 

1. What is Newton's rings phenomenon?

Newton's rings refer to the pattern of concentric circular fringes that are observed when a plano-convex lens is placed on top of a flat glass surface. This phenomenon is caused by the interference of light waves reflected from both surfaces of the lens and the glass plate.

2. How is the radius of curvature calculated for Newton's rings?

The radius of curvature can be calculated using the formula: R = r(n+1/2)λ, where R is the radius of curvature, r is the distance between the center of the lens and the point of contact with the glass plate, n is the order of the bright ring, and λ is the wavelength of the light source.

3. What are the 5th and 15th bright rings in Newton's rings?

The 5th and 15th bright rings refer to the 5th and 15th concentric circular fringes that appear in the pattern of Newton's rings. These rings are used to calculate the radius of curvature of the lens and the flat glass surface.

4. Why are the 5th and 15th bright rings used to calculate the radius of curvature?

The 5th and 15th bright rings are used because they are easily distinguishable and their positions can be accurately measured. This allows for a more precise calculation of the radius of curvature.

5. How is the radius of curvature used in optics?

The radius of curvature is an important parameter in optics as it determines the focal length of a lens. It is also used to calculate the power and magnification of a lens. In addition, the radius of curvature is used in the design and manufacturing of lenses for various optical instruments.

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