chapter 24. optical instruments · 2009-02-02 · and forms a real, inverted image at distance...

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Chapter 24. Optical Instruments Eyeglasses, microscopes and telescopes aid our senses by using lenses and mirrors to form images we wouldn’t be able to see, or see as well, with our eyes alone. Chapter Goal: To understand some common optical instruments and their limitations.

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Lenses in Combination

The analysis of multi-lens systems requires only one new rule: The image of the first lens acts as the object for the second lens.

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The Camera •  A camera lens forms a real

inverted image on a light-sensitive detector in a light-tight box.

•  A adjustable focus combination lens acts as a single lens with an effective focal length

•  The effective focal length is changed by varying the spacing between a converging lens and diverging lens.

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EXAMPLE 24.2 Focusing a camera

QUESTION:

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EXAMPLE 24.2 Focusing a camera

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Human eye


Focusing and Accommodation •  The ciliary muscles to change the curvature of the lens

surface. •  Tensing the ciliary muscles causes accommodation, which

decreases the lens’s radius of curvature and thus decreases its focal length.

•  The farthest distance at which a relaxed eye can focus is called the eye’s far point (FP). The far point of a normal eye is infinity.

•  The closest distance at which an eye can focus, using maximum accommodation, is the eye’s near point (NP), normally 25 cm.

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EXAMPLE 24.4 Correcting hyperopia

QUESTION:

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EXAMPLE 24.5 Correcting myopia

QUESTION:

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EXAMPLE 24.5 Correcting myopia

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The Microscope •  A specimen to be observed is placed on the stage of a

microscope, directly beneath the objective, a converging lens with a relatively short focal length.

•  The objective creates a magnified real image that is further enlarged by the eyepiece.

•  The lateral magnification of the objective is

• Together, the objective and eyepiece produce a total angular magnification

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The Telescope

• A simple telescope contains a large-diameter objective lens which collects parallel rays from a distant object

and forms a real, inverted image at distance s' = fobj. •  The focal length of a telescope objective is very nearly the

length of the telescope tube. •  The eyepiece functions as a simple magnifier. •  The viewer observes an inverted image. •  The angular magnification of a telescope is

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The Telescope


Diffraction effects

A lens both focuses and diffracts light.


The Resolution of Optical Instruments The minimum spot size to which a lens can focus light of wavelength λ is

where D is the diameter of the circular aperture of the lens, and f is the focal length. In order to resolve two points, their angular separation must be greater than θmin, where

is called the angular resolution of the lens.

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Estimate of the angular resolution of the eye.

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This corresponds to resolving two dimes (1 cm) at a distance of 1/(3e-4) = 3e3 cm = 30 m.

The density of rods and cones has evolved to match the diffraction limit.


A moment of appreciation

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The microscope opened the microscopic universe making possible the study of biology at the cellular level.

The telescope opened the celestial universe enabling the discovery of our place in the solar system and in the universe.

Let us not forget too the art of the emulsion photographic film permitting the observation of small dim signals.


A. Causes the light rays to focus closer than they would with the first lens acting alone.

B. Inverts the image but does not change where the light rays focus.

C. Causes the light rays to focus farther away than they would with the first lens acting alone.

D. Prevents the light rays from reaching a focus.

The second lens in this optical instrument

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A. Causes the light rays to focus closer than they would with the first lens acting alone.

B. Inverts the image but does not change where the light rays focus.

C.  Causes the light rays to focus farther away than they would with the first lens acting alone.

D. Prevents the light rays from reaching a focus.

The second lens in this optical instrument

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A.  stay the same B.  be increased C.  be decreased

A photographer has adjusted his camera for a correct exposure with a short-focal-length lens. He then decides to zoom in by increasing the focal length. To maintain a correct exposure without changing the shutter speed, the diameter of the lens aperture should

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A.  stay the same B.  be increased C.  be decreased

A photographer has adjusted his camera for a correct exposure with a short-focal-length lens. He then decides to zoom in by increasing the focal length. To maintain a correct exposure without changing the shutter speed, the diameter of the lens aperture should

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A.  The myopic friend B.  The hyperopic friend C.  Either will do D.  Neither will work

You need to improvise a magnifying glass to read some very tiny print. Should you borrow the eyeglasses from your hyperopic friend or from your myopic friend?

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A.  The myopic friend B.  The hyperopic friend C.  Either will do D.  Neither will work

You need to improvise a magnifying glass to read some very tiny print. Should you borrow the eyeglasses from your hyperopic friend or from your myopic friend?

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A.  Halved. B.  Doubled. C.  Kept the same. D.  The magnification cannot be kept the

same if the objective is changed.

A biologist rotates the turret of a microscope to replace a 20× objective with a 10× objective. To keep the same overall magnification, the focal length of the eyepiece must be

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A.   Halved. B.  Doubled. C.  Kept the same. D.  The magnification cannot be kept the

same if the objective is changed.

A biologist rotates the turret of a microscope to replace a 20× objective with a 10× objective. To keep the same overall magnification, the focal length of the eyepiece must be

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A.  w2 = w3 > w4 > w1 B.  w1 = w2 > w3 > w4 C.  w4 > w3 > w1 = w2 D.  w1 > w4 > w2 = w3 E.  w2 > w1 = w3 > w4

Four diffraction-limited lenses focus plane waves of light with the same wavelength l. Rank order, from largest to smallest, the spot sizes w1 to w4.

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A.  w2 = w3 > w4 > w1 B.  w1 = w2 > w3 > w4 C.  w4 > w3 > w1 = w2 D.   w1 > w4 > w2 = w3 E.  w2 > w1 = w3 > w4

Four diffraction-limited lenses focus plane waves of light with the same wavelength l. Rank order, from largest to smallest, the spot sizes w1 to w4.

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chapter 24. optical instruments · 2009-02-02 · and forms a real, inverted image at distance...

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