Curved glass and Newton's Rings

In summary, the problem involves a curved glass with a radius of 10m, used to form Newton's Rings. There are 100 dark fringes, not including the central dark spot, and the light used has a wavelength of 654 nm. The goal is to find the radius of the outermost dark ring in the pattern. The hint suggests using the equation Sin(theta)= m* lamda/ W, but the provided link may provide more assistance in solving the problem.
  • #1
semper_deere
1
0

Homework Statement


A piece of curved glass has a radius of r=10m and is used to form Newton's Rings. Not counting the dark spot in the center of the pattern, there are one hundred dark fringes the last one on the outer edge of the curved piece of glass. The light being used has a wavelength of 654 nm in a vacuum. What is radius R of the outermost dark ring in the pattern?

Hint:r >> R you may assume Tan(theta)= theta for small angles, where theta must be expressed in radians.
lamda = 654 E-9 m= 100

Homework Equations



the only equation that I can find that is even close is Sin(theta)= m* lamda/ W that is use for single slit diffraction. I really do not know how to set this up. The hint is no help to me at all.
 
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  • #2
I believe the following page should aid you.

http://www.fas.harvard.edu/~scdiroff/lds/LightOptics/NewtonsRings/NewtonsRings.html
 
  • #3




The equation you mentioned, Sin(theta)= m* lamda/ W, is indeed the correct equation to use for this problem. However, it is not the single slit diffraction equation, but rather the equation for the radius of the mth dark ring in Newton's Rings pattern. Theta in this case represents the angle between the center of the curved glass and the mth dark ring.

Using this equation, we can rearrange it to solve for the radius R of the outermost dark ring:

R = (m * lamda) / (2 * Sin(theta))

Since the hint states that r >> R, we can assume that the angle theta is very small, and therefore we can use the approximation Tan(theta) = theta. This simplifies the equation to:

R = (m * lamda) / (2 * theta)

Now, we are given the wavelength lamda = 654 nm and the number of dark fringes m = 100. We can also calculate the angle theta using the radius of the curved glass r = 10m and the distance between the glass and the lens W = r/2 = 5m. Using the small angle approximation, we get:

theta = Tan(theta) = R/W = R/5

Substituting this value of theta into our equation for R, we get:

R = (m * lamda) / (2 * theta) = (100 * 654 E-9) / (2 * R/5)

Solving for R, we get:

R = 5 * 100 * 654 E-9 / (2 * R) = 327 E-6 / R

Multiplying both sides by R, we get the quadratic equation:

R^2 = 327 E-6

Solving for R, we get two possible values: R = +/- 0.018 m. However, since we are looking for the radius of the outermost dark ring, the correct answer is R = 0.018 m. Thus, the radius of the outermost dark ring in the Newton's Rings pattern is 0.018 m or 18 mm.
 

What is curved glass?

Curved glass is a type of glass that has been shaped into a curved or arched surface rather than being flat. This can be achieved through a variety of methods, such as bending, molding, or cutting the glass into a curved shape. Curved glass is commonly used in architectural and design applications, as well as in the production of specialized lenses and mirrors.

What are Newton's Rings?

Newton's Rings are a series of concentric colored rings that are formed when a convex lens is placed on top of a flat glass surface. These rings are caused by the interference of light waves reflecting off of the two surfaces of the glass. They were first observed by Sir Isaac Newton in the 17th century and are used in various scientific applications, such as measuring the thickness of very thin objects.

How are curved glass and Newton's Rings related?

Curved glass and Newton's Rings are related due to the phenomenon of interference that occurs when light passes through or reflects off of curved surfaces. In the case of Newton's Rings, the curved glass surface causes interference patterns to form. This can also be observed in other curved glass objects, such as lenses and mirrors.

What is the significance of Newton's Rings in optics?

Newton's Rings are significant in optics because they provide a method for measuring very small distances, such as the thickness of a thin film. They also demonstrate the principles of interference and can be used to study the properties of light. Additionally, the unique patterns created by Newton's Rings have practical applications in various optical instruments and technologies.

Can Newton's Rings be observed on flat glass surfaces?

No, Newton's Rings can only be observed on curved glass surfaces. This is because the curvature of the glass causes the light waves to interfere with each other, creating the distinctive ring patterns. On a flat glass surface, the light waves do not have the same interference and thus, Newton's Rings cannot be observed.

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