Two similar thin equi-convex lenses, of focal length $f$ each, are kept coaxially in contact with each other s

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 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 :

Accepted Answer

For two lenses in contact, $\frac{1}{F_1} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f} \implies F_1 = \frac{f}{2}$. When glycerine is filled, the combination acts as a single lens of focal length $F_2 = f$. Thus $F_1 : F_2 = \frac{f}{2} : f = 1 : 2$.

Step-by-Step Solution

Practice All PHYSICS Questions