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 F1. When the space

between the two lenses is filled with

glycerine (which has the same refractive index

( = 1.5) as that of glass) then the equivalent

focal length is F2. The ratio F1 : F2 will be ?​

Answer 1

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

To Find: The ratio of $F_1:F_2$

Solution: The ratio of $F_1:F_2$ is $2:1$

Step by step explanation:

Equivalent focal length in air,

$\frac{1}{F_1} =\frac{1}{f} +\frac{1}{f} =\frac{2}{5}$

When glycerin is filled inside, glycerin lens behaves like a diverging lens of focal length (-f),

$:\implies\frac{1}{F_2} =\frac{1}{f}+\frac{1}{f} -\frac{1}{f}$

$=\frac{1}{f}$

$:\implies \boxed{\frac{F_1}{F_2} =\frac{1}{2} }$

Hence, the ratio of $F_1:F_2$ is $1:2$