Question

Two similar thin equiconvex lens of focal length f as 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 are same refractive index musical 21.5 as that of glass than required for calling this f2 then the ratio of f1 and f2 is

Answer 1

The ratio of focal length of lens without or with filling the glycerine in space of the two equi-convex lens is  f1 and f2 respectively is 1 : 2

1. The focal length of the combination of two equi-convex lens when there is no glycerine is
2. $\frac{1}{f1} =\frac{1}{f} +\frac{1}{f}$  f1 =f/2
3. When we fill the gap between two convex lens with glycerine the combination will act like a combination of 3 lenses
4. In which one lens which is formed because of glycerine act like a concave lens with same focal length as other two have
5. The focal length of the combination of two equi-convex lens when there is  glycerine in between is
6. $\frac{1}{f2} =\frac{1}{f} +\frac{1}{f}-\frac{1}{f}=\frac{1}{f}$ f2 = f
7. The ratio of focal length of lens without or with filling the glycerine in space of the two equi-convex lens is  f1 and f2 respectively is
8. $\frac{f1}{f2} =\frac{f/2}{f} =\frac{1}{2}$