Refraction by Spherical Surfaces: Practice Problem & Solution
Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is $F_1$. When the space between the two lenses is filled with glycerine (which has the same refractive index ($\mu = 1.5$) as that of glass) then the equivalent focal length is $F_2$. The ratio $F_1 : F_2$ will be : (2019)
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:
Initially, for two lenses in contact, $1/F_1 = 1/f + 1/f = 2/f$, meaning $F_1 = f/2$.When filled with glycerine, it forms an equi-concave lens of focal length $-f$. The new combination is $1/F_2 = 1/f - 1/f + 1/f = 1/f$, giving $F_2 = f$. The ratio $F_1 : F_2 = (f/2) : f = 1 : 2$.
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