Brief Summary
This YouTube video provides a comprehensive 5-hour review of optics for the ЕГЭ (Unified State Exam) in physics, covering reflection, refraction, lenses, and wave optics. It includes theoretical explanations, problem-solving, and discussions on the relevance of optics in the ЕГЭ. The video also features organizational announcements, such as a giveaway and information about a half-year preparation course.
- Covers entire optics section for ЕГЭ.
- Includes theory and problem-solving.
- Discusses reflection, refraction, lenses and wave optics.
Вступление
The video starts with a greeting and a check to ensure the stream is running correctly, including audio and video. The host introduces himself as Artem Vitalievich from the Shkolkovo educational project, focusing on preparation for the ЕГЭ and physics olympiads. He encourages viewers to like the video and subscribe to the Shkolkovo YouTube channels for general content and physics-specific material, as well as his Telegram channel for updates on ЕГЭ and olympiads in physics.
Организационный момент. Что будет на стриме?
The host outlines the agenda for the 5-hour stream, which includes a розыгрыш (giveaway) for free access to any course for a month, and a comprehensive study of optics. The session will cover the theoretical aspects of optics and include problem-solving. The content is designed for students with varying levels of familiarity with optics, from beginners to those with some prior knowledge. The stream will include breaks, and active participation is encouraged.
Где оптика была в ЕГЭ 2023 и где она может появиться в ЕГЭ 2024?
The video discusses the presence of optics in the ЕГЭ in 2023 and its potential role in the 2024 exam. In 2023, optics appeared in both the first and second parts of the ЕГЭ. The first part included one question worth one point and three questions worth two points each. The second part could include a qualitative problem worth 3 points, a computational problem worth 2 points, and another computational problem worth 3 points. For the 2024 ЕГЭ, there have been changes, reducing the number of tasks in electrodynamics in the first part and removing one problem from the second part.
Что сказали в интервью с составителем ЕГЭ об оптике?
The host shares insights from an interview with a ЕГЭ compiler, who suggested that optics might not be heavily featured in the second part of the exam in 2024. While the official specifications allow for optics questions in the qualitative and computational sections, the compiler indicated a preference for focusing on other topics like MKT (Molecular Kinetic Theory) and electrostatics. The host advises students to primarily prepare for optics in the first part of the ЕГЭ, while those in the course will also prepare for the second part just in case.
О полугодовом курсе. Какие плюсы присоединиться прямо сейчас?
The host promotes a half-year preparation course for the ЕГЭ, which includes access to materials for mechanics, MKT, thermodynamics, electrodynamics, optics, and quantum physics. The course offers personalized study plans and support from tutors. The host addresses concerns about joining the course mid-year, highlighting the benefits of recorded content, such as the ability to speed up, slow down, pause, and use timecodes for efficient learning.
Оптика. Три большие мини-темы: Отражение и преломление света, линзы (геометрическая оптика), волновая оптика
The video outlines the three main topics to be covered in the optics section: reflection and refraction of light, lenses (geometric optics), and wave optics. The host estimates that each section will take about 1.5 hours, including a break. The approach will be a combination of theory and problem-solving.
Оптика. Отражение и преломление лучей
The video transitions to the first main topic: reflection and refraction of light. It begins by stating that light travels in a straight line in a homogeneous medium, where the speed of light is constant.
Однородная среда
A homogeneous medium is defined as one in which the speed of light is constant.
Закон отражения света
The law of reflection states that the angle of incidence equals the angle of reflection. The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
Угол падения и угол отражения
The angle of incidence and the angle of reflection are defined as the angles between the ray and the normal to the surface, not the angle between the ray and the surface itself.
Как работает зеркало
The video explains how mirrors work by discussing how the eye perceives reflected light. When light rays from an object reflect off a mirror and enter the eye, the eye extends these rays backward to form an image. This image appears to be behind the mirror. The image is formed symmetrically to the object relative to the mirror's surface.
Откуда возникает закон отражения света? Принцип Ферма
The video explains the law of reflection using Fermat's principle, which states that light travels between two points in the shortest possible time. In a homogeneous medium, this means light travels in a straight line. Fermat's principle can be used to derive the law of reflection.
Какие задачи с зеркалом ожидать в ЕГЭ 2024? Примеры
The video discusses the types of problems involving mirrors that might appear on the ЕГЭ in 2024. These include scenarios where an object or the mirror is moved, and the task is to determine how the image shifts. The video provides an example where the distance between an object and a mirror is reduced, and the corresponding change in the distance between the object and its image is calculated.
Почему свет преломляется?
The video explains why light refracts, using the principle that light wants to travel from one point to another in the shortest time. When light moves from one medium to another with a different speed of light, it bends to minimize the time spent in the slower medium.
Закон преломления света. Абсолютный показатель преломления, относительный показатель преломления
The video introduces Snell's law, which describes the refraction of light. Snell's law is expressed as ( n_1 \sin(\alpha_1) = n_2 \sin(\alpha_2) ), where ( n ) is the absolute refractive index of the medium and ( \alpha ) is the angle of incidence or refraction. The absolute refractive index indicates how much slower light travels in a medium compared to a vacuum. The relative refractive index describes how much slower light travels in one medium compared to another.
Как вывести закон преломления света
The video derives Snell's law from Fermat's principle. It sets up a scenario with two points, A and B, in different media, and calculates the time it takes for light to travel between them. By minimizing this time using calculus, the video arrives at Snell's law.
Как ведет себя свет при переходе из одной среды в другую?
The video explains how light behaves when transitioning between media with different optical densities. When light moves from an optically less dense medium to a denser one, it bends toward the normal. Conversely, when light moves from an optically denser medium to a less dense one, it bends away from the normal.
Что если угол падения равен нулю?
If the angle of incidence is zero, the light passes straight through without refraction.
Явление полного внутреннего отражения света
The video explains total internal reflection, which occurs when light travels from an optically denser medium to a less dense medium. At a certain critical angle, the angle of refraction reaches 90 degrees. Beyond this angle, light is entirely reflected back into the denser medium. The critical angle is given by ( \sin(\alpha_{\text{critical}}) = \frac{n_2}{n_1} ), where ( n_1 > n_2 ).
Где встречается явление полного внутреннего отражения света?
Total internal reflection is used in fiber optic cables to transmit data. Light travels through the cable by repeatedly reflecting off the walls, allowing for efficient signal transmission over long distances.
Оптика в кодификаторе ЕГЭ 2024
The video reviews the topics in optics listed in the ЕГЭ 2024 codifier, including rectilinear propagation of light, point sources, light rays, the law of reflection, image construction in plane mirrors, the law of refraction, absolute and relative refractive indices, frequency and wavelength relationships, and total internal reflection.
Задача №1 (Луч света падает на плоское зеркало)
A light ray strikes a flat mirror at an angle of incidence of 25 degrees. The angle of reflection is also 25 degrees. The angle between the mirror's surface and the reflected ray is 65 degrees. If the angle of incidence is increased by 5 degrees, the angle between the incident and reflected rays becomes 60 degrees. If the mirror is rotated 5 degrees clockwise, the angle of reflection becomes 35 degrees.
Задача №2 (Предмет высотой 10 см находится на 20 см от плоского зеркала)
An object 10 cm tall is placed 20 cm from a flat mirror. The height of the image is 10 cm, and the distance between the mirror and the image is 20 cm. If the object is moved 4 cm further from the mirror, the distance between the object and its image becomes 48 cm.
Задача №3 (Луч света лазерной указки падает из воздуха)
A laser pointer emits light from air onto a glass surface, where the light travels at 200,000 km/s. The refractive index of the glass is calculated using the formula ( n = \frac{c}{v} ), where ( c ) is the speed of light in a vacuum and ( v ) is the speed of light in the medium. The refractive index of the glass is 1.5.
Задача №4 (Ученик проводит опыт по преломлению света)
A student conducts an experiment on light refraction. As the angle of incidence increases, the angle of refraction also increases, while the refractive index of the glass remains constant.
Задача №5 (Школьник, изучая законы геометрической оптики)
A student studies geometric optics and measures angles of incidence and refraction. The angle of incidence is 70 degrees, and the angle of refraction is 40 degrees. The refractive index of the glass is approximately 1.47.
Задача №6 (Свет идет из вещества с показателем преломления в вакуум)
Light travels from a substance with a refractive index ( n ) into a vacuum. The limiting angle of total internal reflection is 30 degrees. The refractive index ( n ) is calculated using the formula ( n = \frac{\sin(90^\circ)}{\sin(30^\circ)} ), which gives ( n = 2 ).
Задача №7 (Точечный источник света находится в емкости)
A point light source is placed in a container of liquid and lowered vertically. A bright spot appears on the surface of the liquid. The formation of the spot is due to total internal reflection. The refractive index of the liquid is calculated to be approximately 2.24.
Задача №8 (Непрозрачный круг освещается точечным источником света)
An opaque circle is illuminated by a point light source, casting a circular shadow on a screen. The diameter of the circle is 0.1 meters. The distance from the light source to the circle is one-third of the distance from the light source to the screen. The diameter of the shadow is 0.3 meters.
Задача №9 (Точечный источник S расположен вблизи системы)
A point source of light is placed near a system of two mirrors. The system forms two images.
Задача №10 (В плоском зеркале наблюдается изображение стрелки)
An image of an arrow is observed in a flat mirror. To fully see the image of the arrow, the eye needs to be moved one cell to the left.
Розыгрыш
The host conducts a giveaway for ten free one-month subscriptions to any course on the platform.
Перерыв
A 10-minute break is announced.
Линза. Построение лучей. Формула тонкой линзы
The video transitions to the topic of lenses, covering ray tracing and the thin lens formula.
Что такое линза? Линзы собирающие и рассеивающие
A lens is defined as an intersection of spherical surfaces, typically made of glass. Lenses are divided into two types: converging (or convex) lenses and diverging (or concave) lenses. A converging lens converges parallel light rays to a single point, while a diverging lens spreads them out.
Главная оптическая ось
The principal optical axis is the axis perpendicular to the lens surface and passing through the optical center.
Оптический центр
The optical center is the center point of the lens.
Фокус
The focus is the point where parallel light rays converge after passing through a converging lens, or the point from which they appear to diverge after passing through a diverging lens.
Фокусное расстояние
The focal length is the distance from the lens to the focus.
Фокальная плоскость
The focal plane is the plane perpendicular to the principal optical axis that passes through the focus.
Как строить лучи в линзе?
The video explains how to trace rays through lenses:
- A ray parallel to the principal optical axis passes through the focus (or appears to come from the focus for a diverging lens).
- A ray passing through the optical center continues without deviation.
- Any random ray can be traced by constructing a secondary optical axis parallel to the ray, finding the secondary focus, and drawing the ray through that point.
Как строить предмет в любой линзе?
To construct the image of an object in a lens, trace at least two rays from a point on the object. The intersection of these rays (or their extensions) determines the location of the corresponding point on the image.
Расстояние от предмета до линзы
The distance from the object to the lens is denoted as ( d ).
Построение изображений в линзе и их характеристики
The video discusses the characteristics of images formed by lenses, including whether they are real or virtual, upright or inverted, and magnified or diminished.
1. d меньше F
When the object distance ( d ) is less than the focal length ( F ) of a converging lens, the image is virtual, upright, and magnified.
2. d = F
When the object distance ( d ) is equal to the focal length ( F ) of a converging lens, no image is formed.
3. F меньше d меньше 2F
When the object distance ( d ) is between ( F ) and ( 2F ) of a converging lens, the image is real, inverted, and magnified.
4. d = 2F
When the object distance ( d ) is equal to ( 2F ) of a converging lens, the image is real, inverted, and the same size as the object.
5. d больше 2F
When the object distance ( d ) is greater than ( 2F ) of a converging lens, the image is real, inverted, and diminished.
6. Рассеивающая линза
For a diverging lens, the image is always virtual, upright, and diminished, regardless of the object distance.
Формула тонкой линзы
The thin lens formula is given by ( \frac{1}{F} = \frac{1}{d} + \frac{1}{f} ), where ( F ) is the focal length, ( d ) is the object distance, and ( f ) is the image distance. The sign conventions are: ( F ) is positive for converging lenses and negative for diverging lenses; ( f ) is positive for real images and negative for virtual images.
Оптическая сила линзы
The optical power of a lens, denoted as ( D ), is the reciprocal of the focal length: ( D = \pm \frac{1}{F} ). It is measured in diopters (dptr).
Увеличение линзы
The magnification of a lens is the ratio of the image height ( H ) to the object height ( h ): ( \Gamma = \frac{H}{h} = \frac{f}{d} ).
Как работает наш глаз?
The human eye functions as an optical system with the crystalline lens acting as a converging lens and the retina as the screen. The lens focuses light onto the retina, forming a real, inverted, and diminished image. The brain then processes this image.
Задача №11 (Постройте изображения источников)
This task involves constructing images of light sources using a thin converging lens.
Задача №12 (От точечного источника света, находящегося на главной оптической оси)
This problem involves a point light source on the principal optical axis of a thin converging lens.
Задача №13 (На рисунке показан ход двух лучей)
Two rays from a point source pass through a thin lens. The focal length of the lens is 6 cm.
Задача №14 (Какая из точек, показанных на рисунке)
This problem asks to identify the image location of a point source after passing through a lens.
Задача №15 (Какая точка является изображение точки)
This problem asks to identify the image location of a point source after passing through a lens, where the point is located at double focal length.
Задача №16 (В опыте нить накала лампочки расположена вблизи главной оптической оси)
A light bulb filament is placed near the principal optical axis of a thin lens. First, a diverging lens is used, then a converging lens. The image is virtual, diminished, and upright with the diverging lens, and real, equal in size, and inverted with the converging lens.
Задача №17 (Небольшой предмет расположен на главной оптической оси)
A small object is placed on the principal optical axis of a thin converging lens between the focal point and twice the focal point. As the object is moved closer to the focal point, the size of the image increases, and the optical power of the lens remains constant.
Задача №18 (Стеклянную линзу, показанную на рисунке, переносят из воздуха)
A glass lens is moved from air to water. The focal length increases, and the optical power decreases.
Задача №19 (Пучок параллельных световых лучей падает вдоль)
A parallel beam of light rays falls along the principal optical axis onto a thin converging lens with a diameter of 6 cm and an optical power of 5 diopters. A screen is placed 10 cm behind the lens. The diameter of the light spot formed on the screen is 3 cm.
Задача №20 (Предмет высотой 4 см расположен)
An object 4 cm high is placed 30 cm from a thin converging lens. The image height is 8 cm. The focal length of the lens is 20 cm.
Задача №23 (Собирающая линза с фокусным расстоянием 10 см)
A converging lens with a focal length of 10 cm forms a virtual image 15 cm from the lens. The object is 6 cm from the lens, and the distance between the object and the image is 9 cm.
Перерыв
A break is announced.
Волновая оптика
The video transitions to the topic of wave optics.
Распространение волны. Длина волны, свет в вакууме, частота
The video discusses wave propagation, defining wavelength as the distance between two crests. Light is an electromagnetic wave with a wavelength between 400 nm (violet) and 800 nm (red). The relationship between wavelength ((\lambda)), speed ((v)), and frequency ((\nu)) is given by ( \lambda = \frac{v}{\nu} ). The frequency remains constant when light moves from one medium to another.
Интерференция, дифракция, дисперсия
The video introduces three key phenomena in wave optics: interference, diffraction, and dispersion.
Что такое интерференция?
Interference is the superposition of two or more coherent waves.
Когерентные волны
Coherent waves have the same frequency and a constant phase difference.
Синфазные источники
For in-phase sources, the condition for constructive interference (maximum) is that the path difference ((\Delta)) is an integer multiple of the wavelength ((\lambda)): ( \Delta = n\lambda ), where ( n = 0, 1, 2, \dots ). The condition for destructive interference (minimum) is that the path difference is an odd multiple of half the wavelength: ( \Delta = (2n + 1)\frac{\lambda}{2} ).
Дифракция
Diffraction is the bending of waves around obstacles whose size is comparable to or smaller than the wavelength.
Формула дифракционной решетки
The formula for the diffraction grating is ( d \sin(\varphi) = m\lambda ), where ( d ) is the grating period, ( \varphi ) is the angle of diffraction, ( m ) is the order of the maximum, and ( \lambda ) is the wavelength of light.
Задача №26 (Пучок монохроматического света вошел из воздуха в воду)
A beam of monochromatic light enters water from air. The frequency of the electromagnetic oscillations remains unchanged.
Задача №28 (На дифракционную решетку, имеющую 100 штрихов)
A diffraction grating has 100 lines per millimeter. Light with a wavelength of 650 nm is incident on the grating. The maximum order of the diffraction maximum that can be observed is 15.
Задача №33 (В прозрачном сосуде, заполненном водой)
A diffraction grating is placed in a transparent container filled with water. The grating is illuminated with a parallel beam of monochromatic light. If the water is replaced with a liquid with a higher refractive index, the frequency of the light remains unchanged, and the angle between the incident beam and the first diffraction maximum decreases.
Дисперсия
Dispersion is the dependence of the refractive index on the frequency of light. This phenomenon causes white light to separate into a spectrum of colors when passing through a prism.
Заключение
The host concludes the video, thanking viewers for their participation and providing information about upcoming streams and courses.
