Uncategorized: Practice Problem & Solution
37. A plano-convex lens fits exactly into a planoconcave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is: (2013)[cite: 1]
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
For the plano-convex lens, $1/f_1 = (\mu_1 - 1)/R$. For the plano-concave lens, $1/f_2 = -(\mu_2 - 1)/R$.[cite: 1] The focal length of the combination is $1/F = 1/f_1 + 1/f_2 = (\mu_1 - 1 - \mu_2 + 1)/R = (\mu_1 - \mu_2)/R$. Thus, $F = \frac{R}{(\mu_1 - \mu_2)}$.[cite: 1]
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