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Chapter 10: Problem 6

Which of the following lenses would you prefer to use while reading small letters found in a dictionary? (a) A convex lens of focal length \(50 \mathrm{~cm}\). (b) A concave lens of focal length \(50 \mathrm{~cm}\). (c) A convex lens of focal length \(5 \mathrm{~cm}\). (d) A concave lens of focal length \(5 \mathrm{~cm}\).

Short Answer

Expert verified
Option (c) - Convex lens of focal length 5 cm.

Step by step solution

01

- Understand the Purpose of the Lens

To read small letters, a lens that magnifies the text is necessary. Magnifying lenses are typically convex lenses because they can converge light rays to form a magnified image of objects.
02

- Eliminate Options Based on Lens Type

Convex lenses converge light rays, whereas concave lenses diverge them. Since we need a lens that magnifies, concave lenses (options (b) and (d)) can be eliminated.
03

- Compare Focal Lengths of Convex Lenses

Convex lenses with shorter focal lengths provide greater magnification. The two remaining options are:(a) A convex lens of focal length 50 cm.(c) A convex lens of focal length 5 cm.The lens with the shorter focal length (option (c) with 5 cm) will provide greater magnification.
04

- Choose the Most Suitable Lens

Given that greater magnification is better for reading small letters, option (c), a convex lens of focal length 5 cm, is the preferred choice.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

convex lens
A convex lens is also known as a converging lens because it brings light rays together at a point. Convex lenses are thicker in the middle and thinner at the edges.Their ability to converge light makes them ideal for magnification purposes.
Convex lenses are commonly used in:
  • Magnifying glasses
  • Eyeglasses for far-sightedness
  • Cameras
When light passes through a convex lens, it bends toward the principal axis. This makes objects appear larger than they are. The degree of magnification depends on the focal length of the lens.
concave lens
A concave lens, or diverging lens, spreads out light rays that have been refracted through it. These lenses are thinner in the middle and thicker at the edges. Concave lenses are not typically used for magnification.
They are often found in:
  • Eyeglasses for near-sightedness
  • Peepholes
  • Laser beams
When light rays enter a concave lens, they diverge away from each other. This makes objects appear smaller or reduced in size. Since we are looking for a lens to magnify small letters, concave lenses are not suitable.
focal length
The focal length of a lens is the distance from the center of the lens to the focal point, where light rays converge or diverge. It is a crucial factor influencing the lens's magnifying power. Convex lenses with shorter focal lengths provide greater magnification, while longer focal lengths offer less magnification.
Here are some key points about focal length:
  • Shorter focal length = Greater magnification
  • Longer focal length = Less magnification
  • Measured in centimeters (cm) or millimeters (mm)
For our exercise, a convex lens with a focal length of 5 cm provides more magnification than one with a focal length of 50 cm, making it better for reading small letters.

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Most popular questions from this chapter

Name the type of mirror used in the following situations. (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. Support your answer with reason.

An object of size \(7.0 \mathrm{~cm}\) is placed at \(27 \mathrm{~cm}\) in front of a concave mirror of focal length \(18 \mathrm{~cm}\). At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.

A doctor has prescribed a corrective lens of power \(+1.5 \mathrm{D}\). Find the focal length of the lens. Is the prescribed lens diverging or converging?

The magnification produced by a plane mirror is \(+1 .\) What does this mean?

A spherical mirror and a thin spherical lens have each a focal length of \(-15 \mathrm{~cm}\). The mirror and the lens are likely to be (a) both concave. (b) both convex. (c) the mirror is concave and the lens is convex. (d) the mirror is convex, but the lens is concave.
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