Physics II: Chapter 13

Reference: Beginning Physics II

Chapter 13: LIGHT AND OPTICAL PHENOMENA

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KEY WORD LIST

Physical Optics, Geometrical Optics, Refraction, Reflection, Snell’s Law, Critical Angle, Total Reflection, Angle Of Deviation, Dispersion, Rainbow.

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GLOSSARY

For details on the following concepts, please consult Chapter 13.

PHYSICAL OPTICS
In physical optics we treat the phenomena that arise due to the wave nature of the light, as well as interference phenomena.

GEOMETRICAL OPTICS
The phenomena that arise when light can be considered to be adequately described by rays traveling in straight lines (perpendicular to the wave fronts) that change speed in moving from one medium to another. This is the case as long as the objects through which the light travels have dimensions that are much larger than the wavelength of the wave.

REFRACTION
The change of direction of a ray of light in passing obliquely from one medium into another in which its wave velocity is different. We define a quantity called the “index of refraction,” n, in terms of the velocity of light in the material, v, relative to its velocity, c, in a vacuum:

n = c/v

The frequencies of the transmitted and reflected waves are the same as that of the incident waves since the rate of oscillation in the disturbance is precisely what is propagated from one location to the next. Since T = l/f is constant we can calculate the new wavelength as the distance traveled during one period, or

λ’ = vT = vλ/c = λ/n

REFLECTION
The act of casting back the light, mirroring, or giving back or showing an image; the state of being reflected in this way. The angle of reflection equals the angle of incidence, i.e.

θr = θ1

SNELL’S LAW
The angle of refraction is given by

n1 sin θ1 = n2 sin θ2

It is important to note, as can be seen from the geometry in the figure, that the angle of incidence, reflection and refraction also represent the angles that the wave fronts of the incident, reflected and refracted waves respectively make with the surface.

CRITICAL ANGLE
When light travels from a dense (n2) to less dense (n1) medium, the angle of refraction is greater than the angle of incidence. The critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. 

sin θc = n1 / n2

TOTAL REFLECTION
When light is incident from a dense (n2) to less dense (n1) medium, at an angle greater than the critical angle, no light is refracted so all the light must be reflected. We call this case one of “total reflection“. Total reflection is very useful for bending light at a surface without losing any of the energy to transmission through the surface.

ANGLE OF DEVIATION
When the light leaves the prism its direction of motion is at an angle δ from the incident direction. This is the “angle of deviation“.

DISPERSION
For materials there is a small dependence of the velocity of light, and therefore n, on the wavelength. This property is called “dispersion” since it can be used to disperse the various wavelengths that are included in a beam of light into different refractive paths, creating a “spectrum”. As a result of the dispersion, white light refracted in a prism will be separated into its constituent wavelengths after passing through the prism

RAINBOW
A rainbow is another case in which the variation of index of refraction with wavelength leads to a spectrum.

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May 30, 2023 – 1:21 PM Categories: Physics | Post a comment

KHTK Factor # 19

Reference: A Course on the Factors

KHTK Factor # 19: Neither our forms nor our viewpoints are imperishable. They are forever changing.

Our viewpoint can change just as our form can change. Of this we can be sure. 

Bodies die and new bodies are born. The old identity is no longer there. New identities come about. Most of the times this change is gradual. But, at times, it can be quite sudden.

This is natural.

But neither the form nor the viewpoint is unchanging and eternal. There is no permanent individuality.

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Scientology

Compare the above to the following factor in Scientology.

Scientology Factor # 19. And the viewpoint can never perish; but the form can perish. 

That a viewpoint can never perish is a fixed idea of Hubbard. It just happens to be quite prevalent in the society, such as, the soul of a person is considered to be eternal. But this is not verified to be true. Memories may last beyond a lifetime, but this does not verify the eternity of soul.

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Logic

In this universe, absolutes are unattainable. There is no substance that remains unchanging eternally.

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May 30, 2023 – 4:18 AM Categories: KHTK | Post a comment

MN 4 Fear and Dread

Reference: Exploring the Words of the Buddha

This is a summary of MN 4: Fear and Dread (Bhayabherava Sutta)

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MN 4 Summary

(1 – 3) When clansmen have gone forth from the home life into homelessness out of faith in Buddha, they have Buddha for their leader, their helper, and their guide; and they follow the example of Buddha. Remote jungle-thicket resting places in the forest are hard to endure, seclusion is hard to practice, and it is hard to enjoy solitude. One would think the jungles must rob a bhikkhu of his mind, if he has no concentration.

(4 – 19) It is true that unwholesome fear and dread comes under those conditions of homelessness in remote jungle-thickets. However, one finds great solace in dwelling in the forest, as one develops the following qualities:

  1. One is purified in bodily, verbal and mental conduct and livelihood (not unpurified)
  2. One is uncovetous (not covetous and full of lust).
  3. One has a mind of loving-kindness (not with a mind of ill will and intentions of hate)
  4. One is without sloth and torpor (not overcome by sloth and torpor)
  5. One has a peaceful mind (not overcome with restless and unpeaceful mind)
  6. One has gone beyond doubt (not uncertain and doubting)
  7. One is not given to self-praise and disparagement of others
  8. One is free from trepidation (not subject to alarm and terror)
  9. One has few wishes (not desirous of gain, honour, and renown)
  10. One is energetic (not lazy and wanting in energy)
  11. One is established in mindfulness (not unmindful and fully aware)
  12. One is possessed of concentration (not unconcentrated and with straying minds)
  13. One is possessed of practical wisdom (not devoid of wisdom or be a driveller)

(20 – 26) The way to subdue that fear and dread in haunted spaces is to keep the same posture that one is in (walking, standing, sitting, and lying down) until the fear and dread gradually dissipates. Secluded from sensual pleasures and unwholesome states, one enters upon the first jhana and abides in it. He uses mindfulness of breathing as his meditation subject. The applied and sustained thought is present, with rapture and pleasure born of seclusion. With the stilling of applied and sustained thought, one enters upon and abides in the second jhana. There is self-confidence and singleness of mind with rapture and pleasure born of concentration. With the fading away as well of rapture, one enters upon and abides in the third jhana. He is now mindful and fully aware, and has equanimity; though he still feels pleasure with the body. With no fixation on pleasure and pain, and with the previous disappearance of joy and grief, one enters upon and abides in the fourth jhana. Now there is only the purity of mindfulness due to equanimity. There is neither-pain-nor-pleasure. 

(27 – 33) Having gone through the four jhanas, Buddha directed his attention to the recollection of past lives. He recollected many aeons of world-contraction and expansion, and hundred thousand births with their aspects and particulars. This was the first true knowledge that Buddha attained. He then directed his attention to knowledge of the passing away and reappearance of beings. He saw beings inferior and superior, fair and ugly, fortunate and unfortunate passing away and reappearing. He understood how beings pass on according to their actions. This was the second true knowledge that Buddha attained. Next, He directed his attention to knowledge of the destruction of the taints. He came to know very directly, the nature of suffering and taints , their origin, their cessation, and the way leading to their cessation. With this direct knowledge, Buddha’s mind was liberated from the taint of sensual desire, from the taint of being, and from the taint of ignorance. He directly knew: ‘Birth is destroyed, the holy life has been lived, what had to be done has been done, there is no more coming to any state of being.’ This was the third true knowledge that Buddha attained. 

(34 – 35) Buddha was enlightened but he still preferred to resort to remote jungle-thicket resting places in the forest. This was because he saw a pleasant abiding for himself there, and also because he had compassion for future generations (to be an example for them).

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May 29, 2023 – 3:25 PM Categories: Buddhism | Post a comment

KHTK Factor # 18

Reference: A Course on the Factors

KHTK Factor # 18: The human viewpoint sees suffering and survival among these forms, and it endeavors to resolve it through prayer, meditation, art, and science.

The human effort is to make life better by resolving suffering. Prayer is the longing for freedom from suffering. Meditation is an effort to let go of existing conditioning. Art is the search for new viewpoints that go beyond the mundane human existence. Science uses a more systematic approach to covert vision into reality. Here we have the evolution of human thought.

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Scientology

Compare the above to the following factor in Scientology.

Scientology Factor # 18. It is the opinion of the viewpoints that some of these forms should endure. Thus there is survival.

Any opinion must have a purpose underlying it. The purpose to simply create an effect is without substance. It is empty and hollow. 

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Logic

Logic must have the purpose to resolve anomalies; and not just to have opinions to create effect.

The overall purpose is to know and evolve.

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May 29, 2023 – 7:15 AM Categories: KHTK | Post a comment

MN 26 The Noble Search

Reference: Exploring the Words of the Buddha

This is a summary of MN 26: The Noble Search (Ariyapariyesana Sutta).

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MN 26 Summary

(1 – 4) Introduction

(5 – 12) Out of affinity one seeks those things that are similar to him; but this is a form of fixation of attention (attachment). For example, a person is subject to birth, aging, sickness, death, sorrow, and defilement. So, he searches for things that are also subject to birth, aging, sickness, death, sorrow, and defilement. This is ignoble search. The noble search is seeking of nibbana, which offers supreme security from these bondages.

(13 – 14) The young Gautama realized the dangers of the bondages of birth, aging, sickness, death, sorrow, and defilement. He, despite the tearful objections of his parents, shaved off his head, put on yellow robes, and went into homelessness in search of the supreme security of nibbana. 

(15 – 18) The Dhamma of Alara Kalama enabled Gautama to reach the stage of “reappearance in the base of nothingness.” The Dhamma of Uddaka Ramaputta enabled enabled him further to reach the stage of “reappearance in the base of neither-perception-nor-non-perception.” But Gautama was not satisfied because these Dhammas did not lead to the disenchantment, dispassion, cessation, peace, direct knowledge, and enlightenment of Nibbana.” Finally, Gautama settled down to strive on his own. All his effort then paid off. He attained nibbana with the realization, “My deliverance is unshakeable; this is my last birth; now there is no renewal of being.”

(19 – 24) The Dhamma that Gautama realized was specific conditionality, dependent origination, and the stilling of all formations. It could not be attained by mere reasoning. It was too subtle to be experienced even by the wise. Buddha felt that it would be difficult for people to see this truth, as they were so steeped in worldliness. He hesitated at the thought of teaching his Dhamma. Then he reconsidered that there will be those who will understand this Dhamma. Buddha prepared himself for a lifelong commitment. Both Alara Kalama and Uddaka Ramaputta had passed away; so he decided to teach the five monks who were helpful to him while he was striving. He chose them because he thought they would understand his Dhamma quickly.

(25 – 30) Buddha assumed the title of Tathagata—an Accomplished One, a Fully Enlightened One. The Tathagata does not live luxuriously, nor has he given up his striving and reverted to luxury. As Tathagata, Buddha taught his first five disciples. They attained nibbana.

(31 – 37) We learn through our five physical senses. The same senses provide sensual pleasure that is wished for. Connected with it is sensual desire that is provocative of lust. People who are thus stimulated are not under their own control. But, secluded from sensual pleasures, one can maintain applied and sustained thought. This is first jhana. With the stilling of applied and sustained thought, one enters upon the second jhana. Here one has self-confidence and singleness of mind. But there is also the rapture and pleasure born of seclusion. With the fading away as well of rapture there comes equanimity and mindful awareness, and one enters upon the third jhana. But one still feels pleasure with the body. With the abandoning of pleasure and pain, and with the previous disappearance of joy and grief, one enters upon the fourth jhana. 

(38 – 42) With the complete surmounting of perceptions of form, with the disappearance of perceptions of sensory impact, with non-attention to perceptions of diversity, aware that ‘space is infinite,’ one enters upon the base of infinite space. Again, by completely surmounting the base of infinite space, aware that ‘consciousness is infinite,’ one enters upon and abides in the base of infinite consciousness. Again, by completely surmounting the base of infinite consciousness, aware that ‘there is nothing,’ one enters upon and abides in the base of nothingness. Again, by completely surmounting the base of nothingness, one enters upon and abides in the base of neither-pereeption-nor-non-perception. Again, by completely surmounting the base of neither-perception-nor-non-perception, one enters upon and abides in the cessation of perception and feeling. His taints are destroyed by his seeing with wisdom.

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Great Observation

Out of affinity one seeks those things that are similar to him; but this is a form of fixation of attention (attachment).

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May 29, 2023 – 4:57 AM Categories: Buddhism | Post a comment