Refraction by Spherical Surfaces: Practice Problem & Solution
Two identical thin plano-convex glass lenses (refractive index 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the center. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is: (2015)
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:
The focal length of each plano-convex glass lens is $1/f_g = (1.5 - 1)(1/20) = 1/40 cm^{-1}$.[cite: 1] The oil forms an equiconcave lens with $1/f_o = (1.7 - 1)(-2/20) = 0.7(-1/10) = -0.07 cm^{-1}$. The equivalent focal length is $1/F = 1/f_g + 1/f_g + 1/f_o = 2/40 - 0.07 = 0.05 - 0.07 = -0.02 cm^{-1}$. Therefore, $F = -1/0.02 = -50 cm$.
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