Two similar thin equi-convex lenses, of focal length each, are kept coaxially in contact with each other such that the focal length of the combination is . When the space between the two lenses is filled with glycerin (which has the same refractive index () as that of glass) then the equivalent focal length is . The ratio will be:
- A
- B
- C
- D
Solution & Step-by-step Explanation
[Image showing two convex lenses in contact and then with glycerin in the gap]Case 1: .Case 2: Filling the gap creates a third lens (a concave lens) in between.Using Lens Maker's formula for the equi-convex lens (): .The glycerin lens has refractive index and radii of curvature and .Focal length of glycerin lens : .Equivalent focal length .So .Ratio .