Optics Extensions

I. Introduction

A. What is Optics?

B. Section Questions

II. History of Optics

A. Important people and dates

B. Section Questions

III. Nature of Light

IV. Geometrical Optics

A. Reflection and Refraction

1. Snell's Law

2. Prism

3. Critical Angle

B. Spherical and Aspherical Surfaces

C. Lenses

D. Aberration

E. Section Questions

V. Physical Optics

A. Polarization of Light

B. Interference and Diffraction

C. Stimulated Emission

D. Section Questions

VI. Questions

VII. Answers

I. Introduction

A. What is Optics?

The branch of physical science dealing with the propagation and behavior of light is called optics. Light is defined as the part of the electromagnetic spectrum that continues from X rays to microwaves and consists of the glowing force that generates the awareness of vision. In most cases, the study of optics is split into two areas: geometrical optics and physical optics. These branches are studies in great detail in another section.

B. Section Questions (answers on last page)

1. What is the definition of optics?

2. What is the definition of light?

3. What are the two branches of optics?

II. History of Optics

There is not much about the history of optics. Some sources list some important people who have contributed to this field. Others have some dates of important discoveries listed. All that I have found is listed below.

A. Important people and dates

The Dutch mathematician, astronomer, and physical scientist Christiaan Huygens introduced the laws of reflection and refraction of light. They are usually derived using the wave theory of light. He said that every point on an initial wave front might be considered as the source of small, secondary spherical wavelets that spread out in all directions from their centers with the same velocity, frequency, and wavelength as the original wave front.

In 1998, a new discovery was made. A perfect mirror, a mirror that reflected 100 percent of the light that touched it, was made when it was said that it was non-existent. It was made by scientists who stacked up microscopic layers of tellurium and the plastic polystyrene.

Another Dutch scientist who was also a mathematician, Willebrord Snell, came up with a law that states that the product of the refractive index and the sine of the angle of incidence of a ray in one medium is equal to the product of the refractive index and the sine of the angle of refraction in a successive medium. The law goes on to saw that the incident ray, the refracted ray, and the normal to the boundary at the point of incidence all lie in the same plane.

In the late 20^th century, the field of fiber optics benefited from total reflection. If light enters a solid glass or plastic tube obliquely, the light can be totally reflected at the boundary of the tube and eventually come out of the other end. This discovery led to glass fibers being drawn to a very small diameter, coated with a material that reflects easily, and then assembled into flexible bundles or fused into plates of fibers. The flexible bundles, which can be used to provide illumination as well as to transmit images, are valuable in medical examination, as they can be inserted into various openings.

The British physicist, David Brewster, discovered an angle, which he named after himself. If light occurs on a nonabsorbing medium at the so-called Brewster's angle, the reflectance of the factor vibrating parallel to the plane of occurrence is zero. At this angle of incidence, the reflected ray would be perpendicular to the refracted ray, and the tangent of this angle of incidence is equal to the refractive index of the second medium if the first medium is air.

Michael Faraday, whose name was mentioned often in the studies of electricity, magnetism, and electromagnetism, also discovered something pertaining to the field of magnetism and relates to the field of optics. He discovered the Faraday effect. It refers to the fact that a strong magnetic effect across a liquid may cause it to become doubly refracting. This phenomenon is called the Kerr effect, after the British physicist John Kerr.

B. Section Questions (answers on last page)

1. How are the laws of reflection and refraction of light usually derived?

2. In which year was the first perfect mirror made?

3. What was it made out of?

4. What does the Faraday effect refer to?

5. What is this phenomenon called?

6. Who was the Kerr effect named after?

III. Nature of Light

The interactions of light and matter that result in a change in the form of energy are explained by the concept of photons. Photons are packets of energy and follow laws of radiant energy. Transverse waves are used to clarify the spread of light through assorted materials and several of the occurrences of image formation. Transverse waves can be described by points that oscillate in the same plane back and forth across an axis perpendicular to the direction of oscillation. As the wave moves, radiant energy is passes along the axis. The number of complete vibrations in a second on any point on the light wave is called the frequency. Another term used in describing waves is the wavelength.

The linear distance parallel to the axis connecting two points in the same plane is the wavelength. The two points can occupy equivalent positions on the wave. Different colors represent different wavelengths in the electromagnetic spectrum. White light is a mixture of the visible wavelengths. Between different wavelength regions, there is no sharp boundary.

The laws of reflection and refraction of light are usually derived using the wave theory of light introduced by the Dutch mathematician, astronomer, and physical scientist Christiaan Huygens. Huygens's principle states that every point on an initial wave front may be considered as the source of small, secondary spherical wavelets that spread out in all directions from their centers with the same velocity, frequency, and wavelength as the parent wave front. When the wavelets encounter another medium or object, each point on the boundary becomes a source of two new sets of waves. The reflected set travels back into the first medium, and the refracted set enters the second medium. It is sometimes simpler and sufficient to represent the propagation of light by rays rather than by waves. The ray is the flow line, or direction of travel, of radiant energy, and the assumption is made that light does not bend around corners. In geometrical optics the wave theory of light is ignored and rays are traced through an optical system by applying the laws of reflection and refraction.

A. Section Questions (answers on last page)

1. What does the concept of photons explain?

2. What are transverse waves used for?

3. What do different colors represent?

4. What is white light?

IV. Geometrical Optics

Geometrical optics deals with the laws of reflection and refraction of light to aid in the design of lenses and other optical parts of instruments. If a light ray traveling through one uniform medium strikes on the surface of a second uniform medium, a portion of the light is reflected and part may be refracted and enter the second medium. It also may or may not undergo absorption in the second medium.

A. Reflection and Refraction

The amount of light reflected relies on the ratio of the refractive indexes for the two materials. The laws of reflection state that the angle of occurrence is equivalent to the angle of reflection and that the occurrence ray, the reflected ray, and the normal (line perpendicular) to the surface at the point of incidence all lie in the same plane. This is because the plane of incidence contains the occurrence ray and this normal to the surface at the point of occurrence (see Fig. 1). The angle of occurrence (reflection or refraction) is the angle between the occurrence (reflected or refracted) ray and the normal.

This is different in the case of a mirror. A mirror produces reflected images. If the mirror is flat, or plane, the image of the object appears to lie behind the mirror at a distance equal to the distance between the object and the surface of the mirror. The light source in Fig. 2 (point A) sends out light waves which bounce off of the mirror going into directions D and E. The points of contact are B and C respectively. To a person standing in front of the mirror, the light seems to be coming from point F, which is the same distance from the mirror as point A is. Also, according to the laws of reflection, CF and BF form the same angle with the surface of the mirror; the same thing happens to AC and AB. If the surface of the mirror is rough, then the light waves are scattered and go in random directions, therefore not forming an image.

However, not all of the light that strikes a mirror is reflected. Some of the light waves can pass through the mirror or be absorbed by the mirror. It was thought by many scientists that there was no such mirror that could reflect 100 percent of the light. Then, in 1998, scientists made a perfect mirror by stacking up microscopic layers of tellurium and the plastic polystyrene.

1. Snell’s Law

The Dutch mathematician Willebrord Snell, who named it after himself, developed this important law. It states that the product of the refractive index and the sine of the angle of incidence of a ray in one medium is equal to the product of the refractive index and the sine of the angle of refraction in a successive medium. It goes on to state that the incident ray, the refracted ray, and the normal to the boundary at the point of incidence all lie in the same plane.

2. Prism

A prism, a transparent object with flat, polished surfaces at angles to one another, is known to separate or join different wavelengths of light. If light passes through a prism, the exit ray is no longer parallel to the incident ray. This is demonstrated in Fig. 5. A prism can create a spectrum from white light because the refractive index of a material differs for the dissimilar wavelengths. The angle of difference between the rat that enters and the ray that exits is called the angle of deviation.

3. Critical Angle

If a ray is bent away from the normal when it enters a less dense medium and the deviation from the normal increases as the angle of occurrence increases, an angle of incidence exists. It is known as the critical angle, and the refracted ray makes an angle of 90° with the normal to the surface and travels along the boundary between the two materials. If the angle of occurrence is increased more than the critical angle, the light rays will be totally reflected back into the occurrence medium. However, total reflection cannot occur if light is traveling to a denser material. Fig. 6 shows ordinary refraction, refraction at the critical angle, and total reflection. The idea of total reflection was discovered in the late 20^th century to be used in fiber optics. If light enters a solid glass or plastic tube at an angle, the light can be totally reflected from the sides of the tube and continue to be reflected until it comes out of the other end. Glass fibers can be drawn to a very small diameter, coated with a material of lower refractive index, and then assembled into flexible bundles or fused into plates of fibers used to transmit images.

B. Spherical and Aspherical Surfaces

It used to be that most of the expressions of geometrical optics was made keeping spherical reflecting and refracting surfaces in mind. However, aspherical surfaces are sometimes involved. The axis of symmetry is referred to as the optic axis. It passes through the center of a lens or mirror and through the curvature of a spherical object. In this way, if light rays travel parallel to the optic axis, they get reflected or refracted to that they intersect or seem to intersect at a point on the optic axis. This introduces a term called the focal point, which is the distance between this point and the vertex of a mirror or a thin lens. A lens may have two focal lengths, depending on which surface (if the surfaces are not alike) the light strikes first.

There is an equation relationship between the distances measured from the surface of a lens or mirror. If the distances in the direction in which light is traveling are positive and distances measured in the opposite direction are negative, then if is the object distance, the image distance, and is the focal length of a mirror or of a thin lens, the equation applies to spherical mirrors, and the equation applies to spherical lenses. If a simple lens has surfaces with radii and , and the ratio of its refractive index to that of the medium surrounding it is , then .

The focal length can also be determined using a formula. It is equal to half the radius of curvature in the case of a spherical mirror. This is shown in Fig. 7. If the object distance is greater than the distance AC, then the image is real, inverted, and diminished. If the object lies between the center of curvature and the focal point, the image is real, inverted, and enlarged. If the object is located between the surface of the mirror and the focus, the image is virtual, upright, and enlarged. In convex mirrors, only virtual, erect, and diminished images are produced.

C. Lenses

Shorter focal lengths are caused by lenses made with surfaces of small radii. A lens with two convex surfaces always refracts rays parallel to the optic axis. The rays then converge to a focus on the side of the lens that is on the opposite of the object. Concave lenses cause light rays parallel to the optic axis to move away from it, therefore forming virtual, erect, and small images. If the object distance is greater than the focal length, a converging lens forms a real and inverted image. If the object is sufficiently far away, the image is smaller than the object. If the object distance is smaller than the focal length of this lens, the image is virtual, erect, and larger than the object. The angle subtended at the eye by this virtual enlarged image is greater than would be the angle subtended by the object if it were at the normal viewing distance. The ratio of these two angles is the magnifying power of the lens. A lens with a shorter focal length would cause the angle subtended by the virtual image to increase and thus cause the magnifying power to increase.

As the diameter increases, the amount of light a lens can admit increases. The area occupied by an image is proportional to the square of the focal length of the lens. Because of this, the light intensity over the image area is directly proportional to the diameter of the lens and inversely proportional to the square of the focal length. The ratio of the focal length to the effective diameter of a lens is its focal ratio. This is sometimes referred to as the f-number. The reciprocal of this ratio is called the relative aperture. Lenses having the same relative aperture have the same light-gathering power.

D. Aberration

It is predicted by the field of geometrical optics that rays of light originating from a point are imaged by spherical optical parts as a small blur. The outer parts of a spherical surface have a different focal length than does the central area, and this defect would cause a point to be imaged as a small circle. The difference in focal length for the various parts of the spherical section is called spherical aberration. If, instead of being a portion of a sphere, a concave mirror is a section of a paraboloid of revolution, parallel rays incident on all areas of the surface are reflected to a point without spherical aberration. Combinations of convex and concave lenses can help to correct spherical aberration, but this defect cannot be eliminated from a single spherical lens for a real object and image.

The manifestation of differences in lateral magnification for rays coming from an object point not on the optic axis is called coma. If coma is present, light from a point is spread out into a family of circles that fit into a cone, and in a plane perpendicular to the optic axis, the image pattern is comet shaped. Coma may be eliminated for a single object-image point pair, but not for all such points, by a suitable choice of surfaces. Corresponding or conjugate object and image points, free from both spherical aberration and coma, are known as aplanatic points, and a lens having such a pair of points is called an aplanatic lens. Astigmatism is the defect in which the light coming from an off-axis object point is spread along the direction of the optic axis.

If the object is a vertical line, the cross section of the refracted beam is an ellipse that collapses first into a horizontal line, spreads out again, and later becomes a vertical line. If a flat object has any extent, the surface of best focus is curved, or curvature of field results. Distortion arises from a variation of magnification with axial distance and is not caused by a lack of sharpness in the image. Because the index of refraction varies with wavelength, the focal length of a lens also varies and causes longitudinal or axial chromatic aberration. Magnification of different image sizes by various wavelengths is known as lateral chromatic aberration. Converging and diverging lenses grouped together, and combinations of glasses with different dispersions, help to minimize chromatic aberration. Mirrors are free of this defect. In general, achromatic lens combinations are corrected for chromatic aberration for two or three colors.

F. Section Questions (answers on last page)

1. What does geometrical optics help with?

2. What does the amount of light reflected rely on?

3. In which year did scientists make a perfect mirror?

4. What was it made out of?

5. What happens when a ray is bent away from the normal when it enters a less dense medium?

6. Can total reflection occur if light is traveling to a denser material?

7. How does fiber optics work?

8. What kind of image is produced if the object distance is greater than the distance AC in Fig.7?

9. What kind of image is produced if the object lies between the center of curvature and the focal point?

10. What kind of image is produced if the object is located between the surface of the mirror and the focus?

11. What kind of images do convex mirrors produce?

12. What kind of images are produced if the object distance is greater than the focal length?

13. What distance does the object have to be for the image to be smaller than the object?

14. What happens if the object distance is smaller than the focal length of this lens?

V. Physical Optics

Physical optics deals with the study of the polarization of light, interference and diffraction, and the spectral emission, composition, and absorption of light.

A. Polarization of Light

In an ordinary light source, its atoms release pulses of radiation of exceptionally short interval. Each pulse from each atom is an almost monochromatic wave train. The term monochromatic means that it consists of a single wavelength. Also in a regular light source, the angle that the electric vector keeps with the axis across which it oscillates as the wave travels through space stays the same. Another name for this angle is the azimuth. The original azimuth can have any value. Unpolarized light is the effect of the time when large numbers of atoms are emitting photons and the azimuths are randomly distributed. The properties of the light wave are still the same in all directions. If all the azimuths are equal, (or all the transverse waves are located in the same plane,) then the light is said to be polarized.

B. Interference and Diffraction

Two crossing light beams can interfere or interact with each other to affect the resulting intensity pattern. If waves are in the same phase and have the same wavelength, then they are coherent. If the waves do not stay in the same phase and the pattern is random, the waves are incoherent. A greater intensity occurs if the maximum of one wave coincides with the maximum of the others. However, if there is coherence and the maximum of one wave coincides with the minimum of another, they cancel each other out and decrease the intensity. A steady interference pattern can be produced by polarizing the two wave trains in the same plane.

The atoms in an ordinary light source emit photons autonomously; therefore, a large light source usually emits incoherent radiation. Coherent light can be produced by selecting a small portion of the light through a slit or pinhole. Interference patterns can be created from this light by separating this selected light by means of double slits, double mirrors, or double prisms. The two portions of light travel different, but definite paths before they are combined. Equipment that do this are called interferometers. They are used in measuring such things as diameters of stars, distances or thicknesses, and differences of an optical surface from the required shape.

C. Stimulated Emission

Common light sources, the incandescent lamp, fluorescent lamp, and neon lamp, produce incoherent light because emission is impulsive. Simulated emission occurs if enough atoms have absorbed enough energy and become exited to higher states of energy. In this way, light of a certain wavelength can produce additional light of the same wavelength that has the same phase and direction as the original light, which makes it coherent. Stimulated emission amplifies radiation and gives it a very narrow beam spread and a long coherence path. The exited material could be a solid, liquid, or gas, but it must fit an interferometer in which the wavelength being amplified is reflected back and forth many times. A small fraction of the excited radiation is transmitted by one of the mirrors of the interferometers.

There are a couple of acronyms used as terms in this branch of the field of physical optics. For example, maser is an acronym for microwave amplification by stimulated emission of radiation. Laser is an acronym for light amplification by stimulated emission of radiation and is commonly used when optical frequencies are being amplified by stimulated emission. Energizing a large number of atoms to be in the appropriate upper state is called pumping. Pumping can occur either optically or electrically. Laser light is so powerful that it can be reflected off of the moon and detected on earth. Its intense narrow beam is also widely used in surgery and in the cutting of metals.

D. Section Questions (answers on last page)

1. What does the field of physical optics involve?

2. What does monochromatic mean?

3. What value does the original azimuth angle have?

4. What do two crossing light beams do?

5. What does it affect?

6. How can a steady interference pattern be created?

7. How can interference patterns be selected?

8. What are some common light sources?

9. When does simulated emission occur?

10. What states can the exited material me?

11. Which ways can pumping occur?

VI. Questions (answers on last page)

1. Who introduced the laws of reflection and refraction of light?

2. What is a perfect mirror?

3. What did Willebrord Snell do?

4. Which country was he from?

5. Which field benefited from total reflection in the late 20^th century?

6. What happens if light enters a solid glass or plastic tube obliquely?

7. What did David Brewster discover?

8. What did Michael Faraday discover?

9. What are photons?

10. What are transverse waves?

11. What is frequency?

12. What is wavelength?

13. Is there a sharp boundary between different wavelength regions?

14. Which laws do the field of geometrical optics deal with?

15. What happens when if a light ray traveling through one uniform medium strikes on the surface of a second uniform medium?

16. What does the laws of reflection state?

17. Why does this work?

18. What is the angle of occurrence?

19. What kind of images do a mirror produce?

20. Where does the reflected image appear to be if the mirror is flat?

21. What happens if the surface of the mirror is rough?

22. Is an image formed?

23. Does all the light that strikes an ordinary mirror get reflected?

24. What happens to the light waves that do not get reflected?

25. Is there a mirror that can reflect 100 percent of the light waves that strike it?

26. Who was Snell’s Law named after?

27. What does Snell’s Law state?

28. What does a prism do?

29. What happens when light passes through a prism?

30. What is the angle of deviation?

31. Which idea can be used in fiber optics?

32. What is another name for the axis of symmetry?

33. Where is the optic axis located?

34. What is a focal point?

35. Can a lens have two focal lengths?

36. A shorter focal length causes a larger or smaller magnifying power?

37. What is the focal length equal to?

15. Small radii cause the lens to have a long or short focal lengths?

16. Where do rays reflected off of a convex lens surface go?

17. Where do they intersect?

18. Where do rays reflected off of a concave lens surface go?

19. What kind of images are formed?

20. What controls the amount of light that is able to pass through a lens?

21. What is a focal ratio?

22. What is another name for the focal ratio?

23. What is the reciprocal of this ratio?

24. What does an equal relative aperture indicate?

25. What is polarized light?

26. What is the azimuth angle?

27. What is unpolarized light?

28. What are coherent waves?

29. What are incoherent waves?

30. How can the intensity be increased in coherent waves?

31. How can the intensity be decreased in coherent waves?

32. Are the atoms in a light source emitted individually?

33. What kind of light is emitted by a large light source?

34. How can coherent light be produced?

35. What kind of paths does the two sections of light travel?

36. What is the name for equipment that does this?

37. What are they used to measure?

38. What kind of light do common light sources produce?

39. Why does common light give off this kind of light?

40. What does stimulated emission do?

41. What does maser stand for?

42. What does laser stand for

43. What is pumping?

44. What are lasers used for?

Answers

Section I:

38. branch of physical science dealing with the propagation and behavior of light

39. part of the electromagnetic spectrum that continues from X rays to microwaves and consists of the glowing force that generates the awareness of vision

40. geometrical optics and physical optics

Section II:

1. using the wave theory of light

2. 1998

3. stacked up microscopic layers of tellurium and the plastic polystyrene

4. the fact that a strong magnetic effect across a liquid may cause it to become doubly refracting

5. the Kerr effect

6. John Kerr

Section III:

1. the interactions of light and matter that result in a change in the form of energy

2. to clarify the spread of light through assorted materials and several of the occurrences of image formation

3. different wavelengths in the electromagnetic spectrum

4. a mixture of the visible wavelengths

Section IV:

1. the design of lenses and other optical parts of instruments

2. the ratio of the refractive indexes for the two materials

3. 1998

4. microscopic layers of tellurium and the plastic polystyrene

5. an angle of incidence exists

6. no

7. if light enters a solid glass or plastic tube at an angle, the light can be totally reflected from the sides of the tube and continue to be reflected until it comes out of the other end

8. real, inverted, and diminished

9. real, inverted, and enlarged

10. virtual, upright, and enlarged

11. virtual, erect, and diminished

12. sufficiently far away

13. the image is virtual, erect, and larger than the object

14. larger

Section V:

1. study of the polarization of light, interference and diffraction, and the spectral emission, composition, and absorption of light

2. the angle that the electric vector keeps with the axis across which it oscillates as the wave travels through space

3. when large numbers of atoms are emitting photons and the azimuths are randomly distributed

4. interfere or interact with each other

5. the resulting intensity pattern

6. by polarizing the two wave trains in the same plane

7. by separating this selected light by means of double slits, double mirrors, or double prisms

8. the incandescent lamp, fluorescent lamp, and neon lamp

9. when enough atoms have absorbed enough energy and become exited to higher states of energy

10. solid, liquid, or gas

11. optically or electrically

Section VI:

1. Christiaan Huygens

2. a mirror that reflected 100 percent of the light that touched it

3. came up with a law that states that the product of the refractive index and the sine of the angle of incidence of a ray in one medium is equal to the product of the refractive index and the sine of the angle of refraction in a successive medium

4. The Netherlands

5. fiber optics

6. the light can be totally reflected at the boundary of the tube and eventually come out of the other end

7. Brewster's angle

8. the Faraday effect

10. packets of energy

11. points that oscillate in the same plane back and forth across an axis perpendicular to the direction of oscillation

12. number of complete vibrations in a second on any point on the light wave

13. the linear distance parallel to the axis connecting two points in the same plane

14. no

15. laws of reflection and refraction of light

16. a portion of the light is reflected and part may be refracted and enter the second medium

17. the angle of occurrence is equivalent to the angle of reflection and that the occurrence ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane

18. the plane of incidence contains the occurrence ray and this normal to the surface at the point of occurrence

19. the angle between the occurrence ray and the normal

20. reflected

21. behind the mirror at a distance equal to the distance between the object and the surface of the mirror

22. the light waves are scattered and go in random directions

23. no

24. no

25. pass through the mirror or be absorbed by the mirror

26. yes

27. Dutch mathematician Willebrord Snell

28. the product of the refractive index and the sine of the angle of incidence of a ray in one medium is equal to the product of the refractive index and the sine of the angle of refraction in a successive medium, and the incident ray, the refracted ray, and the normal to the boundary at the point of incidence all lie in the same plane

29. separate or join different wavelengths of light

30. the exit ray is no longer parallel to the incident ray

31. the angle of difference between the rat that enters and the ray that exits

32. total reflection

33. optic axis

34. through the center of a lens or mirror and through the curvature of a spherical object

35. the distance between this point and the vertex of a mirror or a thin lens

36. yes

37. half the radius of curvature in the case of a spherical mirror

38. short

39. parallel to the optic axis to a focus on the side of the lens that is on the opposite of the object

40. move away from optic axis

41. virtual, erect, and small images

42. real and inverted

43. the diameter of the lens

44. the ratio of the focal length to the effective diameter of a lens

45. f-number

46. relative aperture

47. same light-gathering power

48. it consists of a single wavelength

49. any value

50. when all the azimuths are equal and all the transverse waves are located in the same plane

51. waves that are in the same phase and have the same wavelength

52. waves that do not stay in the same phase and the pattern is random

53. if the maximum of one wave coincides with the maximum of the others

54. if the maximum of one wave coincides with the minimum of another

55. yes

56. incoherent

57. produced by selecting a small portion of the light through a slit or pinhole

58. different, but definite

59. interferometers

60. diameters of stars, distances or thicknesses, and differences of an optical surface from the required shape

61. incoherent light

62. because emission is impulsive

63. amplifies radiation and gives it a very narrow beam spread and a long coherence path

64. microwave amplification by stimulated emission of radiation

65. light amplification by stimulated emission of radiation

66. energizing a large number of atoms to be in the appropriate upper state

67. in surgery and in the cutting of metals

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