Question:

A plano-convex glass lens $ ({{\mu }_{g}}=3/2) $ of radius of curvature $ R=20\text{ }cm $ is placed at a distance a from a concave lens of focal length 40 cm. What should be the distance b of a point object O from plano-convex lens so that the position of final image is independent of a?

Updated On: Jul 14, 2022
  • 20 cm
  • 60 cm
  • 40 cm
  • 30 cm
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The Correct Option is C

Solution and Explanation

Focal length of the plano-convex lens is $ \frac{1}{f}=({{\mu }_{0}}-1)\left( \frac{1}{20}-\frac{1}{\infty } \right) $ $ =\left( \frac{3}{2}-1 \right)\left( \frac{1}{20} \right)=\frac{1}{2}\times \frac{1}{20} $ $ \Rightarrow $ $ t=40\,cm $ If point object O is placed at a distance of 40 cm from the plano-convex lens, rays become parallel and final image is formed at second focus or 40 cm from concave lens which is independent of a.
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Concepts Used:

Optical instruments

A device that processes light waves (or photons), either to enhance an image for viewing or to analyze and determine its characteristic properties is called an optical instrument (or "optic" for short).

Applications of Optical Instruments:

  1. Microscope - It is one of the most extensively used optical instruments comprised of only one lens or combination of the lenses for magnifying and inspecting bodies that are too small to be seen in detail by clear eyes. Earlier microscopes had only one lens, and are, therefore, called simple microscopes, but the present microscopes are accessible with at least two lenses and thereby, termed a compound microscope.
  2. Telescope - It is another remarkable optical instrument. It makes distant objects emerge nearer by using an arrangement of lenses or lenses and curved mirrors that is used to observe the objects by absorption, emission, and reflection of their electromagnetic radiation to furnish a magnified image. As they are used to view objects that are far away, they include at least two lenses.