Protective equipment for laser safety generally means eye protection in the form of goggles or spectacles, this includes special prescription eyewear using high optical density filter materials or reflective coatings (or a combination of both) to reduce the potential ocular exposure below MPE limits. Some applications, such as use of high power excimer lasers operating in the ultraviolet, may also dictate the use of a skin cover if chronic (repeated) exposures are anticipated at exposure levels at or near the MPE limits for skin.

In general, it is recommended that other controls be employed rather than reliance specifically on the use of protective eyewear. This argument is predicated on the fact that so many accidents have occurred when eyewear was available but not worn. There are many reasons cited for this, but the most common is that laser protective eyewear is often dark, uncomfortable to wear and limits vision

1. Protective Clothing:
Where personnel may be exposed to levels of radiation that clearly exceed the MPE for the skin, particularly in the ultraviolet, the LSO shall recommend or approve the use of protective clothing. Where personnel may be subject to chronic skin exposure from scattered ultraviolet radiation, as may occur during excimer laser processing, skin protection should be provided even at levels below the MPE for the skin. Consideration should also be given to the use of fire resistant material when using Class IV lasers.

2. Laser Barriers and Protective Curtains:
Area control can be effected in some cases using special barriers which have been specifically designed to withstand either direct and/or diffusely scattered beams. In this case, the barrier will exhibit a Barrier Threshold Limit (BTL) for beam penetration through the barrier during some specified exposure time (typically 60 seconds). The barrier is located at a distance from the laser source so that the BTL is not exceeded in the “worst case” exposure scenario. Currently available laser barriers exhibit BTL’s ranging from 10 W/cm(2) to 350 W/cm(2) for different laser wavelengths and power levels. An analysis is usually required (done similarly to the NHZ evaluations) that establishes there commended barrier type and installation distances for a given laser. Important in the design is the factor of flammability of the barrier. It is essential that the barrier not support combustion and be consumed by flames following an exposure.

3. Protective Viewing Windows:
All viewing portals, optics, windows or display screens included as a part of the laser or laser installation shall incorporate some means to attenuate the laser radiation transmitted through the windows to levels below the appropriate MPE levels. This would include, for example, a “viewing window” into the laser facility. The filtration requirements would be based upon the level of laser radiation that would occur at the window in a typical “worst case” condition in a manner identical to the eyewear evaluation.

4. Other Personal Protective Equipment:
Respirators and hearing protection may be required whenever engineering controls cannot provide protection from harmful ancillary environment.

B. Laser Protective Eyeware:
A wide variety of commercially available optical absorbing filter materials (glass and plastics) and various coated reflecting “filters” (dielectric and holographic) are available for laser eye protection. Some are available with spectacle lenses ground to prescription specifications. Protection for multiple laser wavelengths is becoming more common in the research environment as more applications involve several laser types. In this case, dual filters are often the design of choice; frequently mounted in a “flip-up” style goggle or spectacle frame.

The spectral absorption of the filter at the laser wavelength determines the percentage of the beam absorbed by the protective filter. If properly designed, the filter will reduce the “worst case” exposure of the beam to the MPE level. In general, the stronger the filter’s absorption ability, the higher the laser power for which the filter provides protection. This is specified by the filter “optical density” (OD) as is detailed below.

Filters are designed to make use of selective spectral absorption by colored glass or plastic, or selective reflection from dielectric coatings on glass, or both. Each method has its advantages.

Historically, the most common eye protection has been the use of special colored glass absorbing filters. These are generally the most effective in resisting damage from general use as-well-as from exposure to intense laser sources.

Unfortunately, not all absorbing glass filters used for laser protection can be easily annealed (thermally hardened) and, consequently, do not provide adequate impact resistance. In some goggle designs, however, impact resistant plastic filters (polycarbonate) can be used together with non-hardened glass filters in a goggle design where the plastic is placed in front and behind of the non-hardened laser filter glass.

In some tests, glass filter plates have cracked and shattered following intense Q-switched pulsed laser exposures. In some instances, the shattering occurred after one-quarter to one-half hour had elapsed following the exposure. Also, at least one glass filter type has been shown to photobleach when exposed to the short pulses of a Q-switched laser.

The advantage of using reflective coatings is that they can be designed to selectively reflect a given wavelength while transmitting as much of the remaining visible spectrum as possible. However, some angular dependence the of spectral attenuation factor may be present.

The advantages of using absorbing plastic filters materials are greater impact resistance, lighter weight, and convenience of molding the eyeprotection into comfortable shapes. The disadvantages are that they are more readily scratched and the filters often “age” poorly in that the organic dyes used as absorbers are more readily affected by heat and/or ultraviolet radiation which cause the filter to significantly darken. In addition, as will be discussed, the plastic materials generally display a lower threshold for laser beam penetration.

It should be stressed that there are few known materials that can withstand laser exposures which exceed 10(5) W/cm(2) since the electric fields associated with the beam will exceed the bonding forces of matter. Most materials will begin to degrade at levels far below these field strength levels due to thermal or shock effects.

Typical CO(2) laser eyewear products are often made from polycarbonate plastics. These materials are light in weight, relatively inexpensive, and have a high optical density at the 10.6 µm CO(2) wavelength.

It should be noted that such plastic protective eyewear has a penetration threshold level (PTL) of about 5 W/cm(2). It has been shown that for an “arms length” distance of 50 centimeters, the maximum allowed laser beam power limit for a raw beam exposure condition on such plastic eyeprotectors should be less than 20 watts. If beam expansion is present (such as occurs beyond the focus of a simple lens), the power limit is increased to about 200 watts; well above the levels generally experienced without optical enhancement. The upper power limitation for use with plastic eyewear when exposed by a diffuse reflection at 50 cm is well above the power available in commercially available CO(2) lasers.

Therefore plastic eyewear should be acceptable for most laser use situations. It should be strongly noted, however, that the use of plastic eyewear becomes questionable when exposure conditions are closer than “arms length” from the laser and/or under conditions of a direct “raw beam” exposure above a 20 watt level. Such exposures are not likely in most laser facilities; especially for support staff standing at a some distance from the laser. A 20 watt “raw beam” exposure would be far more likely to occur during servicing to the laser equipment or to the operator of a open (Class IV) laser while working at close distances where the irradiance could easily exceed the 5 W/cm(2) limit.

While direct raw beam exposure onto eyewear is certainly not recommended under any normal condition, it does occur. At least one intrabeam eye accident with thermal puncture of plastic laser eyewear has been reported with a Nd:Yag laser in a research laboratory.

Those using CO(2) laser devices should be reminded that materials which do not appear specular (mirror-like) to the eye may be specular at the 10.6 µm far infrared wavelength, e.g., brushed metal surfaces and enamel-metal surfaces. The beam should not be directed near any such surface, particularly if flat. Where possible, optical elements which have convex surfaces to diverge the beam should be used in or near the beam path.

C. Selecting Laser Eyeware:
For all personnel using Class IIIB and Class IV lasers, whether in the production facility, research lab, out-patient clinic or surgical environment must be informed to make the correct and optimum choice of laser protective eyewear.

This means, in general, the need for a more complete understanding of such topics as:

The specific wavelength(s) of the laser emission
Exposure time of anticipated or “worst case” exposure
The output parameters of the laser(s) in use. This includes the average laser power or pulse energy, pulse lengths and pulse repetition characteristics (if applicable).

Worst case ocular exposure levels: either irradiance (W/cm(2)) or radiant exposure (J/cm(2)) of the laser beam.

The “safe” exposure criteria or Maximum Permissible Exposure (MPE) for each laser.

In some cases, aspects of the viewing condition (e.g. point source or extended source).

Reflection factors from targets at the laser wavelength
Optical density (OD) of eyewear at laser output wavelength based above factors.

Visible light transmission requirements
Radiant exposure or irradiance at which laser safety eyewear damage occurs.

  • Need for prescription glasses
  • Comfort and fit
  • Degradation of absorbing media
  • Strength of materials (resistance to shock)
  • Need for peripheral vision
  • Specifications of the protective devices commercially available.

It should be stressed that laser hazards can also include hazards associated with electrical power supplies, flammable or toxic chemicals and materials, fuel hazards, respiratory hazards from laser induced fumes and vapors, and noise hazards. These factors should also be considered in selection of protective equipment; especially eyewear. These conditions may result in hazards from laser related operation (flash tubes, chemicals, fumes, etc.). Consult ANSI Z-87.1: The American National Standard Practice for Occupational and Educational Eye and Face Protection, as-well-as ANSI Z136.1.

It should be noted also that a separate edition of the ANSI standard that pertains only to medical lasers is also available. This edition is ANSI Z136.3 (1988), and is entitled: “Safe Use of Lasers in Health Care Facilities”. This standard addresses the MPE requirements, NHZ specifications, training needs and equipment features, eye and skin protection needs, beam measurement requirements, fume and toxic gas control, equipment and facility audits as-well-as all other appropriate area controls and procedural needs for medical laser usage.

D. Selection Criteria:
The basic requirements for protective eyewear as proposed in the ANSI Z-136.1 standard can be summarized as follows:

Protective eyewear shall be worn whenever operational conditions may result in potential eye hazard.

The attenuation (optical density) of the laser protective eyewear at each laser wavelength shall be specified by the LSO.

All laser protective eyewear shall be clearly labeled with the optical density value and wavelength for which protection is afforded.

Protective eyewear should be comfortable, have adequate visibility (luminous transmission) and prevent hazardous peripheral radiation.

Periodic inspection shall be made of protective eye wear to insure the maintenance of satisfactory filtration ability. This shall include inspection of the filter material for pitting, crazing,cracking, etc. and inspection of the goggle frame for mechanical integrity and light leaks.

The laser parameters of wavelength and exposure time are the most important in determining the maximum permissible exposure (MPE) levels for a specific laser. The ANSI Z-136.1 standard provides charts and tables that allow determination of such levels.

E. Laser Output Factors:
As the laser industry has grown and matured, more lasers have become available with even more complex outputs. Now such exotic terms as: super-pulsed, Q-switched, mode-locked, femtoseconds, Excimers…etc. are used to describe the laser performance. In addition, more safety equipment suppliers provide different types of eye protection; and we hear arguments about alignment versus full protection, plastic versus glass, “laser safe” frames versus untested frames …etc. The eye protection selection process has become more complex as the industry has grown.

The different modes of operation of a laser are distinguished by the rate at which energy is emitted. These include such factors as CW, normal pulse mode, repetitively pulsed, Q-switched and mode-locked. (See Glossary)

These lasers are by no means representative of the vast number of different lasers which are manufactured. It is evident that even these most common laser types produce a wide range of output levels and specific beam characteristics which are dependent in a complex way upon the particular laser media and the manner in which it is operated. This makes a general broad comparison of all laser devices a difficult, if not impossible task, especially for safety eye protection specifications.

For pulsed lasers, the peak power characteristics are all important, and typically, the output specifications are expressed in terms of the pulse energy (Joules) for a given pulse length (seconds). When the output beam is repetitively pulsed, the output beam specifications are usually expressed in terms of average power (Watts), pulse repetition rate (Hertz or pulses-per-second), and single pulse duration (seconds). In addition, the peak power (Watts) of the individual pulse is also often specified. Depending upon design, the beams will, in general, be delivered in a single pulse, in a series of repetitive pulses, or as a continuous wave (CW) level of radiant power.

The major parameters needed when selecting laser protective eyewear are listed below:

WAVELENGTH(S): The wavelength(s) of laser radiation limits the type of eye protection chosen to only that type which reduce the power level at a particular wavelength(s) from reaching the eye at hazardous levels. It is emphasized that many lasers emit more than one wavelength and that each wavelength must be considered. Considering the wavelength corresponding to the greatest output intensity is not always adequate.

For example, a frequency doubled Nd:YAG operating at 0.532 µm may emit about 2 watts at the green wavelength while the Nd:YAG laser itself (operating at 1.064 µm in the near infrared) emits 50 watts. But some safety filters which strongly absorb the 0.532 m wavelength may absorb essentially nothing at the 1.064 µm wavelength. This is big problem for dye lasers which have a variable or tunable wavelength ability. In such cases, the eyewear can only be specified over a narrow band of wavelengths where the therapy is to be done.

OPTICAL DENSITY: Optical density is a parameter for specifying the attenuation afforded by a given thickness of any transmitting medium. Since laser beam intensities may be a factor of a thousand or a million above safe exposure levels, percent transmission notation can be unwieldy and is not used. As a result, laser protective eyewear filters are specified in terms of the logarithmic units of Optical Density (usually referred to as “OD”). The optical density (OD) of a specific filter at a given laser wavelength is related by the equation (see printed copy) where H(o) is the anticipated “worst case” exposure (usually directly out of the laser) and is expressed in the units of W/cm(2) or J/cm(2) depending upon whether the laser in question is CW, repetitively pulsed or single pulse. The MPE is expressed in the identical units as the MPE limit.

It should be noted that since the MPE values are distributed over the pupil diameter (limiting aperture), the calculation for H(o) for beams smaller than the limiting aperture requires that the limiting aperture be used instead of the smaller beam size. That is, the calculation is made as though the beam were spread over the limiting aperture. (See example below.)

Because of the logarithmic factor, a filter attenuating a beam by a factor of 1,000 (or 10(3)) has an optical density of 3, and attenuating a beam by 1,000,000 or (10(6)) has an optical density of 6. The required optical density is determined by the maximum laser beam intensity to which the individual could be exposed. The optical density of two highly absorbing filters when stacked together is essentially the linear sum of two individual optical densities.

LASER BEAM INTENSITY: The maximum laser beam power (Watts) or pulse energy (Joules). In some cases, the beam size is needed where pulsed lasers are expressed in radiant exposure units of Joules/cm(2) and CW lasers in terms of beam irradiance in Watts/cm(2).

VISIBLE TRANSMITTANCE OF EYEWEAR: Since the object of laser protective eyewear is to filter out the laser wavelengths while transmitting as much of the visible light as possible, the visible (or luminous) transmittance should as high as possible. A low visible transmittance (usually measured in percent) creates problems of eye fatigue and may require an increase in ambient lighting. However, adequate optical density at the laser wavelengths should not be sacrificed for improved visible transmittance.

There can be, in some instances, significant differences between the luminous transmission of different filter types for a given laser. In one instance, a specific (green) plastic filter for Nd:YAG lasers has less than 35% visible transmittance while several corresponding glass filters (with only a slight tint) can yield luminous transmissions above 85%. In both cases, adequate OD’s are provided for filtration of the Nd:YAG beam. It is simply more difficult to see through the darker green plastic filters and the clearer glass filter is better suited.

Low visible transmittance has been repeatedly linked with the common practice of “cheating” (i.e., removing the laser eyewear in order to see the area where the beam will hit). This has obvious impact on laser accidents.

LASER FILTER DAMAGE LEVEL: (Maximum Irradiance). At some specific beam intensity, the filter material which absorbs the laser radiation can be damaged. Plastic materials have damage thresholds much lower than glass filters and glass (by itself) is lower than a dielectric coated glass. The damage threshold is especially important for those who work closely to the beam interaction site where there is a much higher probability to receive a direct exposure. Typical damage thresholds for CW lasers fall between 400 and 1000 watts/cm(2) for dielectric coated glass, 100 to 300 watts/cm(2) for uncoated glass and 1 to 10 watts/cm(2) for plastics.

The German eye protection standard (DIN 58 215), for example, requires that both the filter and frame be designed to withstand an exposure of 10 seconds (CW or PRF 10 hz) or 100 pulses (prf hz) without a loss of rated optical density. A similar test exposure criteria is not specifically required by the ANSI Z-136.1 standard, although the standard does indicate that the radiant exposure or irradiance and the corresponding time factors at which damage occurs (penetration), including transient bleaching, is a important factor in determining the appropriate eyewear to be used.

However, unless the eyewear is designed to meet the German DIN standard requirements, damage threshold limits may be difficult to identify and evaluate.

A 1979 FDA study EVALUATION OF COMMERCIALLY AVAILABLE LASER PROTECTIVE EYEWEAR (HEW Publication (FDA) 79-8086) reported limited testing of laser protective eyewear available at that time. For example, tests were reported for Q- switched rubylaser exposures (0.694 µm) on various manufacturer’s protective eyewear. The plasticlaser protective eyewear displayed damage thresholds (surface pitting) ranging from 3.8 to 18 J/cm(2) while glass filters required a radiant exposure ranging from 93 to 1620 J/cm(2).

Detailed damage threshold data for protective eyewear of more recent vintage is not readily available.

F. Optical Density Determination:
Two major factors are required to establish the OD; namely the laser output level and the MPE value for that laser wavelength and at the specified exposure time.

For CW lasers, exposure times can be selected as short as the “blink reflex” time (0.25 second) for some visible lasers; to 10 seconds for some infrared lasers; 600 seconds for viewing diffuse reflections (when they do not act as extended sources). The maximum “worst case” would be an 8 hour (30,000 seconds) exposure that is considered as a maximum daily “occupational” exposure. For pulsed lasers, the individual pulse time is needed and the pulse repetition rate. the MPE value is determined using the ANSI standards. For “worst case” conditions, the beam is considered to be confined to a size of a dark adapted pupil (7 mm). As an example of a single pulse laser, consider the case of an 80 milliJoule single-pulse (50 nanosecond), Q-switched Nd:YAG laser emitted in a 2 mm beam diameter. This would be a Class IV laser and reference to the ANSI Z-136.1 (1986) standard yields an MPE value for a single pulse of: MPE = 5.0 J/cm(2).

The OD is calculated by first determining the value of H(o). From the parameters above, one calculates first the worst case exposure spread over the 7 mm limiting aperture (not the 2 mm beam diameter). The laser beam “area” may be calculated using the equation for a circle as follows: (Equations, see printed copy)

Thus a filter with OD = 4.6 would provide adequate protection for one pulse from this laser.

A wide variety of commercially-available optical filter glass (and plastics) are available for laser eye protection. Some are available in eye-spectacles ground to prescription specifications. One filter-type may be applicable to more than one wavelength. Some filters have a high optical density below a certain “cut-off” wavelength, usually limiting overall visibility.

Consequently, protection devices must be selected based upon the specific operational characteristics of the laser being used. One cannot always be assured that the protective device which may be applicable for one laser will apply to another laser of the same media.

For example, the eyewear OD requirement for a repetitively pulsed, Q-switched Nd:YAG ophthalmic laser WILL NOT BE THE SAME as selected for a 100 watt CW surgical system or, for that matter, for a 15 watt CW Nd:YAG featuring a diffusing probe on a fiber optic delivery. Each unit contains a Nd:YAG laser but each should receive a separate evaluation for optimum laser eye protection because of the system performance differences.

It should be clear that there would be significant difficulty in providing a “one fix – cures all” approach for eyewear selection. The advantages introduced by a broad spectrum of available laser sources is, of itself, a disadvantage when attempting to provide a uniform “all purpose” laser safety code.

G. Eye Protection for Support Staff and Spectators:
Is eye protection needed for the ancillary staff? The answer is YES! In most cases, there can be the possibility of hazardous diffuse reflections and even a diffuse reflection off the wall can exceed the safe exposure limit. If a power less than 500 milliwatts is considered to be a “safe level” to view as a diffuse reflection long-term, and the laser emits 1000 milliwatts, then the potential exposure is well above the safe level, and the beam on the wall could be potentially hazardous to view. The common sense solution is to simply require the use of eye protection.

H. Flashback Filters for Viewing Systems:
Reflections of argon and neodymium laser radiation back through a microscope or endoscope (flash-back) must be attenuated with protective filters built into the optical systems viewer. For example, studies have shown that the reflections back through the laser catheter were of the order of 2 mW for a specular reflection flashback returning through an endoscope PER WATT OF POWER incident at the distal end of the fiber-optic delivery system used with a Nd:YAG laser; and less than 1mW per watt for the argon laser systems.

Thus, filtration would be required to protect the user’s eye from injury during viewing. Computations can show that filters having an optical density of 5.4 would be required at the argon laser wavelengths (assuming a 10 W maximum power) to provide protection as well as comfortable viewing during extended exposures. An optical density of at least 2.1 would be required at the Nd:YAG wavelength assuming 100 watts maximum power.

I. Selection Process:
Selection of laser eyewear first requires an analytical review of a specific laser’s output parameters and selection of the proper maximum permissible exposure limit from the ANSI standard. From this information, the required filter optical density can then be specified using the equation for OD given earlier.

Some will find the logarithmic optical density computation to be beyond their scope of expertise. Those individuals may need to seek assistance from those more experienced in such mathematics or, perhaps, utilize existing computer software programs that are designed to easily provide the answers needed.

1. Alignment Eyeware:
The ultimate choice of eyewear is then made by first making the decision whether “worst case” (so-called full protection) requirements must be met or whether alignment eyewear is needed.

Experience has shown that laser eye accidents more frequently occur during such alignment procedures. A common theme in such laser eye accident has been that AVAILABLE EYE PROTECTION HAS NOT BEEN WORN. There have been numerous accidents reported involving individuals who had eye protection within reach but didn’t have it on. The reason stated was that during “alignment” they need to see the beam! Certainly a reasonable request.

The problem centers on the fact that “full protection” eyewear is usually designed to virtually eliminate the possibility of seeing the beam. Thus a diffuse reflection cannot be seen during an alignment process. As a result, the eyewear is removed to accomplish the alignment task. So called “alignment” eyewear is designed to allow a safe level of laser light to be transmitted through the filter. This requires viewing only diffuse reflections of the beam (scattered light) and never the direct beam. Usually the alignment eyewear does afford some limited-time protection for a direct beam case but it is never intended for such viewing.

Visibility through the filter of the normal ambient light (luminous transmission) can sometimes be improved if the laser eyewear filters are designed for the task. For example, optical alignment with a modestly powerful cw laser can be done using a filter type that reduces the laser power transmitted through the filter from a diffuse reflection to not only a “safe” level but also a level that is “comfortable” to view. This might be required during alignment of an optical system by a technician using a diffusely reflecting target “to see the beam” during the task. In these cases, the MPE used in the optical density determinations can be based upon an exposure time of 600 seconds. Often the design allows an optical density significantly lower than would be required using an 8 hour MPE criteria. This usually results in a filter of greater overall luminous transmission, hence superior visibility while wearing the eyewear.

Since the option during alignment processes is to “cheat” and not wear protective eyewear, in essence, alignment eyewear provides an alternative to no eyewear at all. Clearly a superior alternative considering the accident records!

2. Plastic versus Glass?
Then the concern of plastic versus glass must be considered. This is essentially the question of determining the conditions in which the eyewear is to be used. Namely, is the user to be located in an area where the exposure could exceed the damage threshold (PTL) of the eyewear or is it to be used by ancillary personnel typically at a sufficient distance from the beam interaction site that the PTL requirement is lower.

Obviously cost can play a major role. Laser protective eyewear is not inexpensive. Units can range from about $90.00 for some plastic “goggle” units to over $500.00 for some special coated glass units. Many laser medical facilities purchase a “mix” of units. It should be stressed that the choice of which eyewear to provide should not be based only upon the cost but upon the PROTECTION REQUIREMENT of the individual considering the possibilities for worst case exposure.

The more laser resistant units are normally provided to those regular laser personnel who work close to the beam and the less laser resistant are supplied to those who normally work at a distance from the interaction site. Laser service personnel are usually supplied the more laser resistant eye protection since their activity will bring them in regular close proximity with the beam.

The final choice in the selection process will be the choice in filter types. In some instances there will be a number of possibilities available. In these cases, factors such as room light transmission (luminous transmission) may be the deciding factor. Obviously the higher the luminous transmission the better one can see to do the task.

Many times the final choice will be a trade off between all of the above factors. One may be willing to accept lower luminous transmission but purchase a less expensive eye protector while maintaining the required optical density level. It should go without saying that one should never choose a filter with an inadequate OD rating but one could choose a filter with less white light transmission and have a functional protector.

Additionally, one can consider a “mix” of protectors predicated upon the fact that the protection requirement is not always the same for all laser workers. This approach, however, does impose the need for training for those using the eyewear.

J. Summary:
Reviewing numerous laser accident conditions has shown that having laser eyewear is not the major problem. The major problem is having the laser personnel wear available eyewear.

How does one reinforce the wearing safety eyewear? In any Class IV laser environment the use of eye protection should be a procedural requirement. If laser protective eyewear has been deemed as mandatory for a given procedure, then:


The person who has specific laser safety responsibility of turning on the laser and making sure all the safety features are operational during the process must also be responsible for proper laser eye protection.

One positive aspect that comes from a frequent evaluation of a laser safety program is keeping the level of hazard awareness so high that the personnel wear protective eyewear automatically.

The eyewear selection process first requires basic laser parameter understanding and some fundamental mathematical skills. The decision process is then reduced to an interrelated combination of task analysis, economics and vendor choice.

Guidelines for Laser Safety and Hazard Assessment
Source: Occupational Safety & Health Administration, Guidelines for Laser Safety and Hazard Assessment PUB 8-1.7 (tablular data and equation illustrations have been omitted).