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 glycerin (which has the same refractive index (\(\mu=-1.5\)) as that of glass) then the equivalent focal length is\( F_2.\) The ratio \(F1: F2\) will be: 

• A. \(2:1\)
• B. \(1:2\)
• C. \(2:3\)
• D. \(3:4\)

Answer 1

The Correct Option is B

To find the ratio \(F_1: F_2\) 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 \(f\) each are kept in contact, the focal length \(F_1\) of the combination is given by the formula for combined focal length of lenses in contact:

   \(\frac{1}{F_1} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f}\)

   Thus, \(F_1 = \frac{f}{2}\).

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 \(F_2\) 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:

   \(F_2 = f\)

Now, we can determine the ratio:

\(F_1 : F_2 = \frac{f}{2} : f = 1 : 2\)

Thus, the correct answer is \(1:2\).