In a Newton's rings experiment, if the radius of the nth dark ring is r_n, what is the relationship between r_n and the wavelength λ? (2021)

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Q: In a Newton's rings experiment, if the radius of the nth dark ring is r_n, what is the relationship between r_n and the wavelength λ? (2021)

Solution: The radius of the dark rings in Newton's rings is given by r_n² = nλR, where R is the radius of curvature of the lens. Thus, r_n ∝ nλ.

Steps: 7

Step 1: Understand that Newton's rings are formed by the interference of light between a lens and a flat surface.
Step 2: Recognize that dark rings appear at certain positions where destructive interference occurs.
Step 3: Know that the radius of the nth dark ring is denoted as r_n.
Step 4: Learn the formula that relates the radius of the dark rings to the wavelength of light and the curvature of the lens: r_n² = nλR.
Step 5: Identify that in this formula, n is the ring number, λ is the wavelength of light, and R is the radius of curvature of the lens.
Step 6: From the formula, see that r_n² is directly proportional to n and λ, which means as n or λ increases, r_n² increases.
Step 7: Conclude that the relationship can be simplified to r_n ∝ √(nλ), indicating that the radius of the dark rings increases with both the ring number and the wavelength.