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Chapter 27: Problem 81

An optical system consists of two lenses, one with a focal length of \(0.50 \mathrm{cm}\) and the other with a focal length of \(2.3 \mathrm{cm}\). If the separation between the lenses is \(12 \mathrm{cm},\) is the instrument a microscope or a telescope? Explain.

Short Answer

Expert verified
The instrument is a microscope.

Step by step solution

01

Identify the focal lengths

Determine which lens has a shorter focal length (objective lens) and which has a longer focal length (eyepiece lens). Given focal lengths are 0.50 cm and 2.3 cm. The shorter focal length is 0.50 cm, and the longer one is 2.3 cm.
02

Determine Lens Arrangement

In an optical instrument, a microscope typically has the objective lens with the smaller focal length and placed close to the object, with the eyepiece lens having the larger focal length. In a telescope, the objective lens has the longer focal length and the eyepiece the shorter one.
03

Evaluate the Lenses of the System

Compare the placement and focal lengths from the problem setup. The given system has the shorter focal length of 0.50 cm first, acting as the objective lens, and the longer focal length of 2.3 cm second, as the eyepiece lens.
04

Conclusion on the Instrument Type

Since the system has the configuration of a shorter focal length objective and a longer focal length eyepiece, it fits the specifications for a microscope rather than a telescope.

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Key Concepts

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

Focal Length
The focal length of a lens is a crucial component in optical systems. It refers to the distance over which parallel rays of light either converge to a point or appear to diverge from a point. Understanding focal length helps in determining how a lens will focus light and form images.
  • A shorter focal length lens bends light rays sharply, bringing them to a closer focus point. This characteristic makes it suitable for forming magnified images, as is needed in microscopes.
  • Lenses with longer focal lengths allow light rays to converge at a distance, suitable for applications requiring less magnification, such as in telescopes.
Focal length plays a key role in deciding whether an optical system functions as a microscope or a telescope. By identifying which lens in the setup has the shorter focal length, we can infer its job in the optical arrangement.
Microscope
Microscopes are optical instruments designed for magnifying small objects, making them appear much larger to the observer. They use a combination of lenses to achieve this high level of magnification. The typical microscope includes:
  • **Objective Lens**: This lens, typically with a very short focal length, is placed near the object being observed. Its role is to collect light from the object and create an enlarged image.
  • **Eyepiece Lens**: Positioned closer to the observer's eye and having a longer focal length, the eyepiece magnifies the image created by the objective lens, adding another layer of enlargement for the user.
In the given problem, with a lens configuration where the shorter focal length of 0.50 cm acts as the objective and the longer 2.3 cm focal length lens as the eyepiece, it confirms the optical system is set up as a microscope rather than a telescope. This demonstrates the typical setup of high magnification achieved by placing the short focal length lens closer to the object.
Telescope
Telescopes are designed for viewing distant objects, like stars or planets. Unlike microscopes, they do not aim to achieve high magnification through proximity but rather through different lens arrangements. The configuration typically includes:
  • **Objective Lens**: This lens gathers light from the distant object. It usually has a long focal length to capture as much detail as possible.
  • **Eyepiece Lens**: A shorter focal length lens that refines the image collected by the objective lens. By manipulating the image size, it provides a magnified view of distant scenes.
In telescopes, the objective lens is the one with the longer focal length, contrary to a microscope. Therefore, by swapping the focal lengths (the longer focal length lens comes first), we could transform the given setup into what resembles a telescope configuration. However, as the current problem states the short focal length lens is first, it supports a microscope setup over a telescope.

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Most popular questions from this chapter

Intracorneal Ring An intracorneal ring is a small plastic device implanted in a person's cornea to change its curvature. By changing the shape of the cornea, the intracomeal ring can correct a person's vision. (a) If a person is nearsighted, should the ring increase or decrease the cornea's curvature? (b) Choose the best explanation from among the following: I. The intracorneal ring should increase the curvature of the cornea so that it bends light more. This will allow it to focus on light coming from far away. II. The intracorneal ring should decrease the curvature of the cornea so it's flatter and bends light less. This will allow parallel rays from far away to be focused.

Two thin lenses have refractive powers of +4.00 diopters and -2.35 diopters. What is the refractive power of the two if they are placed in contact? (Note that these are the same two lenses described in the previous problem.)

The Moon has an angular size of \(0.50^{\circ}\) when viewed with unaided vision from Earth. Suppose the Moon is viewed through a telescope with an objective whose focal length is \(53 \mathrm{cm}\) and an eyepiece whose focal length is \(25 \mathrm{mm}\). What is the angular size of the Moon as seen through this telescope?

IP You are taking a photograph of a horse race. A shutter speed of 125 at \(f / 5.6\) produces a properly exposed image, but the running horses give a blurred image. Your camera has \(f\) -stops of \(2,2.8,4,5.6,8,11,\) and \(16 .\) (a) To use the shortest possible exposure time (i.e., highest shutter speed), which \(f\) -stop should you use? (b) What is the shortest exposure time you can use and still get a properly exposed image?

The focal length of the human eye is approximately \(1.7 \mathrm{cm} .\) (a) What is the \(f\) -number for the human eye in bright light, when the pupil diameter is \(2.0 \mathrm{mm} ?\) (b) What is the \(f\) -number in dim light, when the pupil diameter has expanded to \(7.0 \mathrm{mm} ?\)
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