2. (5p) Find the apparent depth $h_i$ as a function of $n_1$, $n_2$, and $h_o$ in the small angle approximation (see below). SHOW YOUR WORK. \begin{align*} \frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f} \qquad m = \frac{h_i}{h_o} = -\frac{d_i}{d_o} \\ n_1 \sin \theta_1 = n_2 \sin \theta_2 \\ \tan \theta \approx \sin \theta \end{align*}
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First, we need to find the angle of incidence (θ1) and the angle of refraction (θ2) using the small angle approximation and Snell's Law. Using the small angle approximation, we have: tan(θ1) ≈ sin(θ1) ≈ θ1 tan(θ2) ≈ sin(θ2) ≈ θ2 Now, using Snell's Law: ni * Show more…
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