Refraction by Spherical Surfaces: Practice Problem & Solution
Two identical glass ($\mu_g = 3/2$) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water ($\mu_w = 4/3$). The focal length of the combination is: (2016 - II)
Solution Explained:
To solve this problem, we apply the core principles of Refraction by Spherical Surfaces. Understanding the underlying formula is key to arriving at the correct answer below:
For the glass lenses, $1/f = (3/2 - 1)(2/R) = 1/R$, so $R = f$.[cite: 1] The water layer forms an equiconcave lens with $1/f_w = (4/3 - 1)(-2/R) = -2/(3R) = -2/(3f)$. The total power is $1/F = 1/f + 1/f + 1/f_w = 2/f - 2/(3f) = 4/(3f)$. Thus, $F = 3f/4$.[cite: 1]
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