2019 Ray Optics and Optical InstrumentsLens Maker's Formula and Combination of Lenses Hard Question 34 of 89 in Ray Optics and Optical Instruments

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 glycerin (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:

A $2:1$
B $1:2$
C $2:3$
D $3:4$

The answer is B.

Solution

In air, the two lenses in contact: $\frac{1}{F_1}=\frac{1}{f}+\frac{1}{f}=\frac{2}{f}$ When glycerine ($\mu=1.5$, same as glass) fills the space, the glycerine forms a concave lens of focal length $-f$: $\frac{1}{F_2}=\frac{1}{f}+\frac{1}{f}-\frac{1}{f}=\frac{1}{f}$ $\frac{F_1}{F_2}=\frac{f/2}{f}=\frac{1}{2}$ $F_1:F_2=1:2$

Concept focal length of a lens combination with a liquid layer

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89 questions from this chapter have appeared across 25 exam years.