Question

Two similar thin equiconvex 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 $\left(\mu =1.5\right)$ as that of lens, 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

Answer 1

The correct option is B 1 : 2

$\frac{1}{F_1}=\frac{1}{f}+\frac{1}{f}\Rightarrow F_1=\frac{f}{2}$
The space between convex lenses filled with glycerin will act as concave lens of focal length -$f$.
$\frac{1}{F_2}=\frac{1}{f}+\frac{1}{f}-\frac{1}{f}\Rightarrow F_2=f\Rightarrow \frac{F_1}{F_2}=\frac{1}{2}$