Raymond A. SerwayChris Vuille

Optical Instruments

1

Analysis generally involves the laws of reflection and refraction.

Analysis uses the procedures of geometric optics (Ray model of light).

However, To explain certain phenomena, the wave nature of light must be used.

Introduction2

The single-lens photographic camera is an optical instrument.

ComponentsOpaque, light-tight boxConverging lens

Produces a real imageFilm behind the lens

Receives the image

Section 25.13

Image is formed on an electric device CCD – Charge-coupled

device CMOS – Complementary

metal-oxide semiconductor

Both convert the image into digital form.

The image can be stored in the camera’s memory.

Section 25.14

Proper focusing leads to sharp images.The lens-to-film distance will depend on the object

distance and on the focal length of the lens.The shutter is a mechanical device that is

opened for selected time intervals.Most cameras have an aperture of adjustable

diameter to further control the intensity of the light reaching the film.With a small-diameter aperture, only light from the

central portion reaches the film, and spherical aberration is minimized.

Section 25.15

Light intensity is a measure of the rate at which energy is received by the film per unit area of the image.The intensity of the light reaching the film is

proportional to the area of the lens.The brightness of the image formed on the

film depends on the light intensity.Depends on both the focal length and the

diameter of the lens

Section 25.16

The ƒ-number of a camera is the ratio of the focal length of the lens to its diameter.ƒ-number = f/DThe ƒ-number is often given as a description of

the lens “speed”.A lens with a low f-number is a “fast” lens.

Section 25.17

8

Increasing the setting from one ƒ-number to the next higher value decreases the area of the aperture by a factor of 2.

The lowest ƒ-number setting on a camera corresponds to the aperture wide open and the maximum possible lens area in use.

Simple cameras usually have a fixed focal length and a fixed aperture size, with an ƒ-number of about 11.The high value of ƒ allows for a large depth-of-field.Most cameras with variable ƒ-numbers adjust them

automatically.

Section 25.1

Example of depth of field

9

10

The normal eye focuses light and produces a sharp image.

Essential parts of the eye Cornea – light passes

through this transparent structure

Aqueous Humor – clear liquid behind the cornea

Section 25.211

The pupilA variable aperture An opening in the iris

The crystalline lensMost of the refraction takes

place at the outer surface of the eye.Where the cornea is covered

with a film of tears

Section 25.212

The iris is the colored portion of the eye.It is a muscular diaphragm that controls pupil

size.The iris regulates the amount of light entering

the eye by dilating the pupil in low light conditions and contracting the pupil in high-light conditions.

The f-number of the eye is from about 2.8 to 16.

Section 25.213

The cornea-lens system focuses light onto the back surface of the eye.This back surface is called the retina.The retina contains receptors called rods and cones.These structures send impulses via the optic nerve

to the brain.The brain converts these impulses into our conscious

view of the world.

Section 25.214

Rods and Cones Chemically adjust their sensitivity according

to the prevailing light conditionsThe adjustment takes about 15 minutes.This phenomena is “getting used to the dark”

Accommodation The eye focuses on an object by varying the

shape of the crystalline lens through this process.

An important component is the ciliary muscle which is situated in a circle around the rim of the lens.

Thin filaments, called zonules, run from this muscle to the edge of the lens.

Section 25.215

The eye can focus on a distant object.The ciliary muscle is

relaxed.The zonules tighten.This causes the lens to

flatten, increasing its focal length.

For an object at infinity, the focal length of the eye is equal to the fixed distance between lens and retina.This is about 1.7 cm

Section 25.216

The eye can focus on near objects.The ciliary muscles tense.This relaxes the zonules.The lens bulges a bit and the focal length

decreases.The image is focused on the retina.

Section 25.217

The near point is the closest distance for which the lens can accommodate to focus light on the retina.Typically at age 10, this is about 18 cm.Average is about 25 cmIt increases with age, to 500 cm or more at

age 60.The far point of the eye represents the

largest distance for which the lens of the relaxed eye can focus light on the retina.Normal vision has a far point of infinity.

Section 25.218

Eyes may suffer a mismatch between the focusing power of the lens-cornea system and the length of the eye.

Eyes may beFarsighted

Light rays reach the retina before they converge to form an image

NearsightedPerson can focus on nearby objects but not those far

away

Section 25.219

Also called hyperopiaThe image focuses behind the retina.Can usually see far away objects clearly,

but not nearby objectsSection 25.2 20

A converging lens placed in front of the eye can correct the condition.

The lens refracts the incoming rays more toward the principle axis before entering the eye. This allows the rays to converge and focus on the retina.

Section 25.2 21

Also called myopiaIn axial myopia the nearsightedness is caused by

the lens being too far from the retina.In refractive myopia, the lens-cornea system is

too powerful for the normal length of the eye.Section 25.2 22

A diverging lens can be used to correct the condition.

The lens refracts the rays away from the principle axis before they enter the eye. This allows the rays to focus on the retina.Section 25.2 23

Presbyopia is due to a reduction in accommodation ability. The cornea and lens do not have

sufficient focusing power to bring nearby objects into focus on the retina.

Condition can be corrected with converging lenses

In astigmatism, the light from a point source produces a line image on the retina. Produced when either the cornea or

the lens or both are not perfectly symmetric

Can be corrected with lenses having different curvatures in two mutually perpendicular directions

Section 25.224

Optometrists and ophthalmologists usually prescribe lenses measured in diopters.The power of a lens in diopters equals the

inverse of the focal length in meters.

Section 25.225

A simple magnifier consists of a single converging lens.

This device is used to increase the apparent size of an object.

The size of an image formed on the retina depends on the angle subtended by the eye.

Section 25.326

When an object is placed at the near point, the angle subtended is a maximum. The near point is about 25 cm

When the object is placed near the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image.

Section 25.3 27

Angular magnification is defined as

The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye.q = - 25 cmCalculated by

Section 25.328

With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrations.

With multiple lenses, magnifications of up to about 20 can be achieved.The multiple lenses can correct for aberrations.

Section 25.329

A compound microscope consists of two lenses. Gives greater magnification than a single lens The objective lens has a short focal length, ƒo<1 cm. The ocular lens (eyepiece) has a focal length, ƒe, of a few

cm.Section 25.4 30

The lenses are separated by a distance L.L is much greater than either focal length.

The approach to analysis is the same as for any two lenses in a row.The image formed by the first lens becomes the

object for the second lens.The image seen by the eye, I2, is virtual,

inverted and very much enlarged.

Section 25.431

The lateral magnification of the microscope is

The angular magnification of the eyepiece of the microscope is

The overall magnification of the microscope is the product of the individual magnifications

Section 25.432

The ability of an optical microscope to view an object depends on the size of the object relative to the wavelength of the light used to observe it.For example, you could not observe an atom (d

0.1 nm) with visible light (λ 500 nm).

Section 25.433

Two fundamental types of telescopesRefracting telescope uses a combination of

lenses to form an image.Reflecting telescope uses a curved mirror and

a lens to form an image.Telescopes can be analyzed by considering

them to be two optical elements in a row.The image of the first element becomes the

object of the second element.

Section 25.534

The two lenses are arranged so that the objective forms a real, inverted image of a distant object.

The image is near the focal point of the eyepiece.

The two lenses are separated by the distance ƒo + ƒe which corresponds to the length of the tube.

The eyepiece forms an enlarged, inverted image of the first image.

Section 25.5 35

The angular magnification depends on the focal lengths of the objective and eyepiece.

Angular magnification is particularly important for observing nearby objects.Very distant objects still appear as a small

point of light.

Section 25.536

Large diameters are needed to study distant objects.

Large lenses are difficult and expensive to manufacture.

The weight of large lenses leads to sagging which produces aberrations.

Section 25.537

Helps overcome some of the disadvantages of refracting telescopesReplaces the objective lens with a mirrorThe mirror is often parabolic to overcome

spherical aberrations.In addition, the light never passes through

glass.Except the eyepieceReduced chromatic aberrations

Section 25.538

The incoming rays are reflected from the mirror and converge toward point A. At A, a photographic

plate or other detector could be placed.

A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece.

Section 25.539

Reflecting TelescopesLargest in the world are 10 m diameter Keck

telescopes on Mauna Kea in HawaiiLargest single mirror in US is 5 m diameter

instrument on Mount Palomar in CaliforniaRefracting Telescopes

Largest in the world is Yerkes Observatory in WisconsinHas a 1 m diameter

Section 25.540

The ability of an optical system to distinguish between closely spaced objects is limited due to the wave nature of light.

If two sources of light are close together, they can be treated as non-coherent sources.

Because of diffraction, the images consist of bright central regions flanked by weaker bright and dark rings.

Section 25.641

If the two sources are separated so that their central maxima do not overlap, their images are said to be resolved.

The limiting condition for resolution is Rayleigh’s Criterion.When the central maximum of one image falls

on the first minimum of another image, they images are said to be just resolved.

The images are just resolved when their angular separation satisfies Rayleigh’s criterion.

Section 25.642

If viewed through a slit of width a, and applying Rayleigh’s criterion, the limiting angle of resolution is

For the images to be resolved, the angle subtended by the two sources at the slit must be greater than θmin

Section 25.643

Section 25.644

The diffraction pattern of a circular aperture consists of a central, circular bright region surrounded by progressively fainter rings.

The limiting angle of resolution depends on the diameter, D, of the aperture.

Section 25.645

If λ1 and λ2 are nearly equal wavelengths between which the grating spectrometer can just barely distinguish, the resolving power, R, of the grating is

A grating with a high resolving power can distinguish small differences in wavelength.

Section 25.646

The resolving power increases with order number. R = Nm

N is the number of lines illuminated.m is the order number.

All wavelengths are indistinguishable for the zeroth-order maximum.m = 0 so R = 0

Section 25.647

The Michelson Interferometer is an optical instrument that has great scientific importance.

It splits a beam of light into two parts and then recombines them to form an interference pattern.It is used to make accurate length

measurements.

Section 25.748

A beam of light provided by a monochromatic source is split into two rays by a partially silvered mirror M.

One ray is reflected to M1 and the other transmitted to M2.

After reflecting, the rays combine to form an interference pattern.

The glass plate ensures both rays travel the same distance through glass.

Section 25.749

The interference pattern for the two rays is determined by the difference in their path lengths.

When M1 is moved a distance of λ/4, successive light and dark fringes are formed.This change in a fringe from light to dark is

called fringe shift.The wavelength can be measured by counting the

number of fringe shifts for a measured displacement of M.

If the wavelength is accurately known, the mirror displacement can be determined to within a fraction of the wavelength.

Section 25.750

51

52

53

(Continued)

54