Geometric Optics Lecture One PDF

Geometric Optics Lecture One Dr. Mohamed Mostafa Physics Department Faculty of Physics Mansoura University 22/10/2024  Nature of light Many theories are made to describe the nature of light.  Nature of light I- New...

Geometric Optics Lecture One Dr. Mohamed Mostafa Physics Department Faculty of Physics Mansoura University 22/10/2024  Nature of light Many theories are made to describe the nature of light.  Nature of light I- Newton’s Theory Light is made up of tiny particles called ‘corpuscles’ having negligible mass. Advantages The corpuscular theory can be explained the reflection and refraction of light. Limitations Corpuscular theory of Newton’s cannot explain the phenomena of diffraction, interference, and polarization of light. II- Christian Huygens’s The light is made up of waves vibrating up and down perpendicular to the direction of the light travels. Advantages The Huygens’s theory can be explained the reflection, refraction and diffraction of light. Limitations -Huygens’s theory cannot explain the phenomena of shadows, interference, and polarization of light. - Huygens’s theory cannot prove that the light wave not required to medium to travel through it.. III- James Clerk Maxwell Light is form of electromagnetic wave (include electric and magnetic field). Advantages - The Maxwell’s theory prove that the light wave not required to medium to travel through it. - The Maxwell’s theory can be explained the reflection, refraction, interference and diffraction of light. Limitations Maxwell theory cannot explain the phenomena of absorption, scattering, emission, and photoelectric effect.  Nature of light IV- Max Plank Light is quanta of energy called photon and each photon has energy (𝑬) depend on the frequency of light (𝒇) as shown in the following relation: 𝑬 = 𝒉 ∗ 𝒇 = 𝒉 𝒄ൗ𝝀 In which, h is Plank constant, 𝝀 is the wave length of light, and 𝒄 is the speed of light in vacuum. Advantages The Plank’s theory can be explained the absorption, scattering, emission, and photoelectric effect.  The photoelectric effect The photoelectric effect is the emission of electrons from the metal surface or within the material when photons (light) hit the metal surface. When photons (light) hit the metal surface, the electron absorbed some of photon energy and utilized it as: Work function (W): Kinetic energy:  The photoelectric effect Work function (W): is the minimum energy needed to remove or liberate an electron from a metal. Kinetic energy: 𝟎. 𝟓 𝒎 𝒗𝟐 In which, 𝒎 is mass of electron, 𝒗 is the velocity of electron  Geometric Optics Geometric optics , which might better be called ray optics , is concerned with the light ray. ‫يستخدم الضوء الهندسى عندما يمثل الضوء بخطوط‬.‫مستقيمة (أشعه) ترسم على الورقة‬ ‫‪Geometric Optics‬‬ ‫يهتم الضوء الهندسى بتفاعل الضوء مع العدسات (‪)Lens‬‬ ‫والمرايا (‪ )Mirrors‬والمنشورات (‪.)Prisms‬‬  Lecture one (1.2) Reflection of light ‫إنعكاس الضوء‬  Reflection of light Laws of Reflection: First Law: The incident ray, the reflected ray and the normal ray at the point of incidence on the reflecting surface are all in the same plane. Second Law: The angle of incidence is equal to the angle of reflection.  ‫‪Reflection of light‬‬ ‫قاعده فيرمات (‪)Fermat’s Principle‬‬ ‫تنص قاعده فيرمات على ان المسار الضوئى الذى يسلكة شعاع‬ ‫من الضوء بين نقطتين فى وجود اكثر من وسط ضوئى يجب ان‬ ‫ياخذ اقل زمن ممكن‪.‬‬ ‫‪light travels between two points along the path‬‬ ‫‪that requires the least time.‬‬ ‫ونظرا الن سرعه الضوء كبيره جدا فبناء على قاعده فيرمات‬ ‫𝑻‪ⅆ‬‬ ‫يكون التغير فى الزمن بالنسبة للمسافة يساوى صفر‪= 𝟎.‬‬ ‫𝒙‪ⅆ‬‬  ‫اشتقاق قانون االنعكاس باستخدام قاعدة فيرمات‪:‬‬ ‫‪S‬‬ ‫‪P‬‬ ‫𝑪‪𝑻 = (𝑺𝑶 + 𝑶𝑷)/‬‬ ‫‪h‬‬ ‫𝟐 𝜽 𝟏𝜽‬ ‫‪b‬‬ ‫طبقا لقاعده فيرمات‬ ‫‪x‬‬ ‫‪O‬‬ ‫‪a‬‬ ‫)𝑷𝑶(‪ⅆ𝑻 𝟏 ⅆ(𝑺𝑶) 𝟏 ⅆ‬‬ ‫=‬ ‫‪+‬‬ ‫𝟎=‬ ‫𝒙‪ⅆ𝒙 𝒄 ⅆ‬‬ ‫𝒙‪𝒄 ⅆ‬‬ ‫= 𝐎‪S‬‬ ‫𝟐𝒙 ‪𝒉 𝟐 +‬‬ ‫= 𝑷𝑶‬ ‫𝟐)𝒙 ‪𝒃𝟐 + (𝒂 −‬‬ Reflection of light ⅆ(𝑺𝑶) 𝟐 𝟐 −𝟏/𝟐 𝒙 = 𝒙(𝒉 + 𝒙 ) = 𝟐 ⅆ𝒙 (𝒉 + 𝒙𝟐 )𝟏/𝟐 ⅆ(𝑶𝑷) − (𝒂 − 𝒙) = 𝟐 ⅆ𝒙 (𝒃 + (𝒂 − 𝒙)𝟐 )𝟏/𝟐 ‫طبقا لقاعده فيرمات‬ ⅆ𝑻 𝟏 ⅆ(𝑺𝑶) 𝟏 ⅆ(𝑶𝑷) = + =𝟎 ⅆ𝒙 𝒄 ⅆ𝒙 𝒄 ⅆ𝒙  Reflection of light 𝒙 (𝒂 − 𝒙) 𝟐 𝟐 𝟏/𝟐 = 𝟐 (𝒉 + 𝒙 ) (𝒃 + (𝒂 − 𝒙)𝟐 )𝟏/𝟐 S P s𝐢𝐧 𝜽𝟏 = s𝐢𝐧 𝜽𝟐 h 𝜽𝟏 𝜽 𝟐 b 𝜽𝟏 = 𝜽𝟐 x O a  Chapter one (1.3) Refraction of light ‫إنكسار الضوء‬  Refraction of light Laws of refraction: 𝜇1 Angle of Angle of First Law: The incident ray, the Incidence Reflection 1 reflected ray and the normal ray at the point of incidence on the 𝜇2 refracting surface are in the same 2 plane. Angle of Refraction Second Law: The ratio of the sine of the angle of incidence to the sine of angle of refraction is a constant which is equal to the relative refractive index of the second medium with respect to the first medium. (sin 𝜃1 / sin 𝜃2 = constant).  Refraction of light Snell law Snell law can be described by the following relation: 𝒔𝒊𝒏 (𝜽𝟏 ) 𝝁𝟐 = 𝒔𝒊𝒏 (𝜽𝟐 ) 𝝁𝟏 EX (1): A light wave passes from air (𝝁𝟏 = 1) to water (𝝁𝟐 = 1.33). If the angle of incidence is 30º, what is the angle of refraction?  𝒔𝒊𝒏 (𝜽1 ) 𝝁2 𝒔𝒊𝒏 (30) 1.33 = = 𝒔𝒊𝒏 (𝜽2 ) 𝝁1 𝒔𝒊𝒏 (𝜽2 ) 1 0.5 = 1.33 𝒔𝒊𝒏 (𝜽2 ) 𝜽2 = 22.1𝑶 EX (2): In the following figure, calculate the index of refraction for medium B? 𝜇1 =1.5  Refraction Problem (4) Calculate the angle of refraction in the lower medium.  Refraction Problem (1&2) A light ray travels from air (𝝁𝟏 = 1.0) into water (𝝁𝟐 = 1.33). The angle of incidence is 34°. What is the angle of refraction? A light ray travels from water into air. If the angle of refraction is 56°, what is the angle of incidence?  ‫‪Refraction of light‬‬ ‫‪S‬‬ ‫اشتقاق قانون االنكسار باستخدام قاعدة فيرمات‪:‬‬ ‫‪Air‬‬ ‫𝑷𝑶 𝑶𝑺‬ ‫=𝑻‬ ‫‪+‬‬ ‫‪h‬‬ ‫𝑪‬ ‫‪V‬‬ ‫‪i‬‬ ‫‪x‬‬ ‫‪a-x‬‬ ‫‪O‬‬ ‫= 𝑶𝑺‬ ‫𝟐)𝒙 ‪𝒉𝟐 + (𝒂 −‬‬ ‫‪r‬‬ ‫‪b‬‬ ‫= 𝑷𝑶‬ ‫𝟐𝒙 ‪𝒃𝟐 +‬‬ ‫‪P‬‬ ‫)𝑷𝑶(‪ⅆ𝑻 𝟏 ⅆ(𝑺𝑶) 𝟏 ⅆ‬‬ ‫=‬ ‫‪+‬‬ ‫𝟎=‬ ‫𝒙‪ⅆ𝒙 𝑪 ⅆ‬‬ ‫𝒙‪𝑽 ⅆ‬‬ Refraction of light ⅆ(𝑺𝑶) 𝟏 −(𝒂 − 𝒙) = ⅆ𝒙 𝑪 (𝒃𝟐 + (𝒂 − 𝒙)𝟐 )𝟏/𝟐 ⅆ(𝑶𝑷) 𝟏 𝒙 = ⅆ𝒙 𝑽 (𝒉𝟐 + 𝒙𝟐 )𝟏/𝟐 ‫طبقا لقاعده فيرمات‬ 𝟏 𝒙 𝟏 (𝒂 − 𝒙) 𝟐 𝟐 𝟏/𝟐 = 𝑽 (𝒉 + 𝒙 ) 𝑪 (𝒃𝟐 + (𝒂 − 𝒙)𝟐 )𝟏/𝟐  Refraction of light S 𝟏 𝒙 𝟏 (𝒂 − 𝒙) Air 𝑽 (𝒉𝟐 + 𝒙𝟐 )𝟏/𝟐 = 𝑪 (𝒃𝟐 + (𝒂 − 𝒙)𝟐 )𝟏/𝟐 h i x a-x O 𝒔𝒊𝒏 𝒓 𝒔𝒊𝒏 𝒊 r = b 𝑽 𝑪 𝒔𝒊𝒏 𝒊 𝑪 P = =𝝁 𝒔𝒊𝒏 𝒓 𝑽  Laws of Geometric Optics Refractive index (μ) Is the ratio of speed of light in vacuum to speed of light in a medium " 𝐂 𝛍= 𝐯 The refractive index is dimensionless number and greater than unity (1) Laws of Geometric Optics if light passes from one medium to another, its frequency doesn't change but its wavelength changes. 𝐂 𝛍𝟏 = 𝒗𝟏 𝐂 𝛍𝟐 = 𝒗𝟐 Laws of Geometric Optics The relation between the optical path difference and the phase difference. 𝟐𝛑 𝐩𝐡𝐚𝐬𝐞 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞 = ∗ 𝐨𝐩𝐭𝐢𝐜𝐚𝐥 𝐩𝐚𝐭𝐡 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞 𝛌 Snell's law : 𝛍𝟏 𝐬𝐢𝐧 𝛉𝟏 = 𝛍𝟐 𝐬𝐢𝐧 𝛉𝟐  Laws of Geometric Optics Huygens's Principle : All points on a given wave front are taken as sources of spherical secondary waves, called wavelets, which propagate outward through a medium with speeds characteristic of waves in that medium. After some time interval has passed, the new position of the wave front is the surface tangent to the wavelets " as shown in the figure :  Laws of Geometric Optics Huygens's Principle : If the distance of the source is small, the wavefront is spherical. If the source is at a large distance, the wavefront is plane.