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Chapter 24: Optical Instruments

•Combinations of Lenses

•The Camera

•The Eye

•The Magnifier

•The Compound Microscope

•The Telescope

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24.1 Combinations of LensesWith lenses in combination, the image formed by one lens is the object for the next lens.

The thin lens equation still applies.

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222

111

111

111

qspfqp

fqp

−=

=+

=+ p is the object distance, q is the image distance, f is the focal length and s is the distance between the lenses.

It is possible to have the object for the second lens be virtual (p2<0); here the image formed by the first lens is beyond the second lens.

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The magnification of a combination of lenses is just the product of the magnifications for the individual lenses.

nmmmm 21total =

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Example: A converging and a diverging lens, separated by a distance of 30.0 cm, are used in combination. The converging lens has f1 = 15.0 cm and the diverging lens has an unknown focal length. An object is placed at 20.0 cm in front of the converging lens; the final image is virtual and is formed 12.0 cm before the diverging lens. What is the focal length of the diverging lens?

111

111fqp

=+ Given: p1 = 20 cm; f1 = 15 cm. Then q1 = 60 cm

Given: s = 30.0 cm. Then p2 = −30 cm.

Given: q2 = −12 cm and p2 = −30 cm. Then f2 = −8.6 cm.222

111fqp

=+

12 qsp −=

24.2 The Camera

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A camera forms a real, inverted image. For far away objects, the film must be placed one focal length from the lens.

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24.3 The Eye

The lens is at a fixed distance from the retina (unlike in some cameras where this is adjustable). The lens has a variable focal length, which is adjusted to keep the image distance (q) constant as the object distance (p) varies.

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The near point is the closest distance from your eye that an object can be seen clearly. For a normal eye this distance is 25 cm.

Refractive power of a lens is defined as:

The far point is farthest distance from your eye that an object can be seen clearly. For a normal eye this distance is ∞.

fP 1=

where f is the focal length of the lens; typical units of P are diopters (1D = 1 m-1).

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For a near sighted (myopic) person, light rays converge before they strike the retina.

A diverging lens is placed in the light path. This creates a virtual image closer to your eye than the actual object is.

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For a far sighted (hyperopic) person, light rays converge after they strike the retina.

A converging lens is placed in the light path. This creates a virtual image farther from your eye than the actual object is.

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Example: If Harry has a near point of 1.5 m, what focal length contact lenses does he require?

The near point refers to the closest distance an object can be to see it clearly, in this case 1.5 m. A normal eye has a near point of 25 cm. These corrective lenses must take an object at 25 cm and form a virtual image at a distance of 1.5 m.

fqp111

=+ Given p = 25 cm; q = −1.5m. Here f = +30.0 cm

The refractive power of these lenses is D 3.3

m 30.011

+===f

P (Diopter)

Harry is farsighted.

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24.4 The Simple Magnifier

For an object to look bigger the image of it formed on the retina must be made bigger.

The farther an object is from your eye, the smaller it will look.

Using the triangles in the figure, the angular size θ of an object is:

distanceobject object of sizetan =≈θθ

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The angular magnification is .unaided

aided

θθ

=M

The largest angular size an object can have and still be seen clearly is when it is placed at your near point.

Nh

==distanceobject

object of sizeunaidedθ

Now the object is placed at the focal point of a converging lens

fh

==distanceobject

object of sizeaidedθ

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fN

Nh

fh

M ===unaided

aided

θθ

N is the near point for a person (typically 25 cm) and f is the focal length of the lens used in the magnifier.

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24.5 The Compound Microscope

The objective lens forms an enlarged real image here.

Two converging lenses are used to produce a highly magnified image.

The eyepiece is used to view this image.

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The eyepiece is used as a magnifier; the image formed by the objective is placed at the focal point of the eyepiece. The total magnification is the product of the individual magnifications:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−==

eyeobjeyeobjtotal f

NfLMmM

where L = “tube length” = q0 − f0; N = near point distance; and fobj & feye are focal lengths of the objective and eyepiece respectively.

Fig. 24.17

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Example: A microscope has an objective lens of focal length 5.00 mm. The objective forms an image 16.5 cm from the lens. The focal length of the eyepiece is 2.80 cm.

(a) What is the distance between the lenses?

Using the figure, the distance between the lenses is d = feye + qo = 2.80 cm + 16.5 cm = 19.3 cm.

(b) What is the angular magnification? The near point is 25.0 cm.

286eyeobj

obj

eyeobjeyeobjtotal

−=⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−==

fN

ffq

fN

fLMmM

o

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24.6 The Telescope

A telescope is a combination of lenses and/or mirrors used to collect a large amount of light and bring it to a focus.

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A refracting telescope (or refractor) uses lens.

The barrel (or tube) length is

.eyeobj ffL +=

The angular magnification is

.eye

obj

obj

eye

ff

M −==θθ

Example: A refracting telescope is used to view the moon (diameter of 3474 km & distance from Earth 384,500 km). The focal lengths of the objective and eyepiece are +2.40 m and +16.0 cm, respectively.

(a) What should be the distance between the lenses?

m 56.2eyeobj =+= ffL

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(b) What is the diameter of the image produced by the objective?

( ) cm 17.2m 3474 km 384,500

m 2.40sizeobject size image

=⎟⎠

⎞⎜⎝

⎛−=−=′

−=′

==

hpqh

pq

hhm

(c) What is the angular magnification?

15m 0.16m 40.2

eye

obj −=−=−=ff

M