Images Formed By Lenses

To find the ratio for the lens system described, we need to consider two cases:

1. Two Lenses in Contact: When two similar thin equi-convex lenses with focal length each are kept in contact, the focal length of the combination is given by the formula for combined focal length of lenses in contact:

   Thus, .

2. Space Filled with Glycerin: When the space between the two lenses is filled with glycerin having the same refractive index as the glass of the lenses, the two lenses effectively act as a single lens with focal length equivalent to infinity. Therefore, the combination focal length becomes the effective focal length of the two lenses considering the entire system as one lens:

   Since the refractive index of glycerin is the same as glass, the focusing effect of the system is halved, so:

Now, we can determine the ratio:

Thus, the correct answer is .