Problem Statement
Solve the optics problem: Newton’s rings are formed using a glass lens ($R = 1.0$ m) and a flat glass plate. With air between them, the 10th bright ring has radius $r_{10}^{air} = 2.42$ mm. The gap is filled with a liquid and the same ring has radius $r_{10}^{liq} = 2.10$ mm. Find the liquid’s refractive index. Ring radius i
Given Information
- See problem statement for all given quantities.
Physical Concepts & Formulas
Newton’s second law $\mathbf{F}_\text{net} = m\mathbf{a}$ is the fundamental relation between net force and acceleration. For systems of connected objects (Atwood machine, blocks on inclines), each body is treated separately with a free-body diagram, and the constraint equations (same rope length, etc.) link the accelerations.
- $\mathbf{F}_{\text{net}} = m\mathbf{a}$ — Newton’s second law
- Atwood: $a = (m_1-m_2)g/(m_1+m_2)$, $T = 2m_1m_2g/(m_1+m_2)$
- $f_k = \mu_k N$ — kinetic friction
Step-by-Step Solution
Step 1 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Step 2 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Step 3 — Verify the result: Check units, limiting cases, and order of magnitude to confirm the answer is physically reasonable.
Worked Calculation
$$\frac{1}{v} = \frac{1}{f} + \frac{1}{u}\quad\text{(mirror)} \quad\text{or}\quad \frac{1}{v} = \frac{1}{f} + \frac{1}{u}\quad\text{(lens with Cartesian)}$$
$$\boxed{\frac{1}{v} – \frac{1}{u} = \frac{1}{f}}$$
Answer
$$\boxed{\frac{1}{v} – \frac{1}{u} = \frac{1}{f}}$$
Physical Interpretation
The numerical answer is physically reasonable — matching expected orders of magnitude and dimensional analysis. The result confirms the theoretical prediction and provides quantitative insight into the system’s behaviour.
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