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

Updated On: Jun 23, 2024
  • 2 : 3
  • 3:4
  • 2 : 1
  • 1:2
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The Correct Option is D

Solution and Explanation

Equivalent focal length in air $\frac{1}{F_{1}} = \frac{1}{f} + \frac{1}{f} = \frac{2}{f} $
When glycerin is filled inside, glycerin lens behaves like a diverging lens of focal length (-f)
$ \frac{1}{F_{2}} = \frac{1}{f} + \frac{1}{f} - \frac{1}{f} $
$ = \frac{1}{f}$
$ \frac{F_{1}}{F_{2}} = \frac{1}{2} $
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Concepts Used:

Spherical Lenses

Lenses that are made by combining two spherical transparent surfaces are called spherical lenses.  In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.

Properties of Convex lens:

  1. In this, the lenses are thicker in the middle and thinner at the edges.
  2. They have a positive focal length.
  3. It intersects the incident rays towards the principal axis
  4. These lenses are used in the camera, focus sunlight, projector microscope, simple telescope, overhead projector, magnifying glasses, etc.

Properties of Concave lens:

  1. These lenses are thinner in the middle and thicker at the edges.
  2. They have a negative focal length.
  3. It parts the incident rays away from the principal axis.
  4. These are used in the glasses, spy holes, some telescopes in the doors, etc.