Question

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 $(p=1.5)$ as that of glass) then the equivalent focal length is $F_2$. The ratio $F_1$ : $F_2$ will be :

• A. 2 : 3
• B. 3:4
• C. 2 : 1
• D. 1:2

Answer 1

Answer: (D)

Equivalent focal length in air $\frac{1}{F_1}=\frac{1}{f}+\frac{1}{f}=\frac{2}{f}$
When glycerin is filled inside, glycerin lens behaves like a diverging lens of focal length (-f)
$\frac{1}{F_2}=\frac{1}{f}+\frac{1}{f}-\frac{1}{f}$
$=\frac{1}{f}$
$\frac{F_1}{F_2}=\frac{1}{2}$