Tiêu đề 09. RAY OPTICS AND OPTICAL INSTRUMENTS.pdf ✅

Blue lakes, ochre deserts, green forest, and multicolored rainbows can be enjoyed by anyone who has eyes with which to see them. But by studying the branch of physics called optics, which deals with the behavior of light and other electromagnetic waves, we can reach a deeper appreciation of the visible world. A knowledge of the properties of light allows us to understand the blue color of the sky and the design of optical devices such as telescopes, microscopes, cameras, eyeglasses, and the human eye. The same basic principles of optics also lie at the heart of modern developments such as the laser, optical fibers, holograms, optical computers, and new techniques in medical imaging. Properties Of Light (i) Speed of light in vacuum, denoted by c, is equal to 3 × 108 m/s approximately. (ii) Light is electromagnetic wave (proposed by Maxwell). It consists of varying electric field and magnetic field. (iii) Light carries energy and momentum. (iv) The formula v = f is applicable to light. (v) When light gets reflected in same medium, it suffers no change in frequency, speed and wavelength. (vi) Frequency of light remains unchanged when it gets reflected or refracted. (a) Regular Reflection: When the reflection takes place from a perfect plane surface it is called Regular reflection. In this case the reflected light has large intensity in one direction and negligibly small intensity in other directions. (b) Diffused Reflection: When the surface is rough, we do not get a regular behavior of light. Although at each point light ray gets reflected irrespective of the overall nature of surface, difference is observed because even in a narrow beam of light there are many rays which are reflected from different points of surface and it is quite possible that these rays may move in different directions due to irregularity of the surface. This process enables us to see an object from any position. Such a reflection is called as diffused reflection. CHAPTER – 9 RAY OPTICS AND OPTICAL INSTRUMENTS RAY O P T I CS AND O P T I C AL INSTR U M E N T S
Laws Of Reflection (a) The incident ray, the reflected ray and the normal at the point of incidence lie in the same plane. This plane is called the plane of incidence (or plane of reflection). This condition can be expressed mathematically as R . (  × N ) = N . (  × R ) =  . ( N × R ) = 0 where  , N and R are vectors of any magnitude along incident ray, the normal and the reflected ray respectively. (a) The angle of incidence (the angle between normal and the incident ray) and the angle of reflection (the angle between the reflected ray and the normal) are equal, i.e. ∠i =∠r Special Cases: Normal Incidence: In case light is incident normally, i = r = 0 δ = 180o Grazing Incidence: In case light strikes the reflecting surface tangentially, i = r = 90 δ = 0o or 360o Object And Image Object- Object is defined as point of intersection of incident rays. Let us call the side in which incident rays are present as incident side and the side in which reflected ( refracted) rays are present, as reflected (refracted) side. Image (): Image is defined as point of intersection of reflected rays (in case of reflection) or refracted rays (in case of refraction). Reflection from a wall, from a newspaper. This is why you cannot see your face in newspaper and in the wall. Example DO YOU KNOW? In vacuum all the different colors of light travels with the same speed. We say that the ray has retraced its path Note In case of reflection speed (magnitude of velocity) of light remains unchanged but in Grazing incidence velocity remains unchanged Note An object is called real if it lies on incident side otherwise it is called virtual. Note An image is called real if it lies on reflected or refracted side otherwise it is called virtual. Note
Plane Mirror Plane mirror is formed by polishing one surface of a plane thin glass plate. It is also said to be silvered on one side. A beam of parallel rays of light, incident on a plane mirror will get reflected as a beam of parallel reflected rays. (i) Distance of object from mirror = Distance of image from the mirror. (ii) All the incident rays from a point object will meet at a single point after reflection from a plane mirror which is called image. (iii) The line joining a point object and its image is normal to the reflecting surface. (iv) For a real object the image is virtual and for a virtual object the image is real (v) The in region which observer's eye must be present in order to view the image is called field of view. Spherical Mirror Spherical Mirror Is formed by polishing one surface of a part of sphere. Depending upon which part is shining the spherical mirror is classified as (a) Concave mirror, if the side towards center of curvature is shining and (b) Convex mirror if the side away from the center of curvature is shining. Important terms related with spherical mirrors : (a) Center of Curvature (c) : The center of the sphere from which the spherical mirror is formed is called the Center of curvature of the mirror. It is represented by C and is indicated in figure. (b) Pole (P) : The center of the mirror is called as the Pole. It is represented by the point P on the mirror APB in figure. (c) Principle Axis : The PRINCIPLE Axis is a line which is perpendicular to the plane of the mirror and passes through the pole. The principle Axis can also be defined as the line which joins the Pole to the Center of Curvature of the mirror. (d) Aperture (a) : he aperture is the segment or area of the mirror which is available for reflecting light. In figure. APB is the aperture of the mirror. (e) Principle focus (F) : It is the point of intersection of all the reflected rays for which the incident rays strike the mirror (with small aperture) parallel to the PRINCIPLE axis. In concave mirror it is real and in the convex mirror it is virtual. The distance from pole to focus is called focal length. Concave mirror Convex mirror Sign Convention We are using co–ordinate sign convention. (i) Take origin at pole (in case of mirror) or at optical center (in case of lens) Take X axis along the Principal Axis, taking positive direction along the incident light. u, v, R and f indicate the x coordinate of object, image, center of curvature and focus respectively. (ii) y-co-ordinates are taken positive above Principle Axis and negative below Principle Axis’ h1 and h2 denote the y coordinate of object and image respectively.
Formulae For Reflection from Spherical Mirrors (i) Mirror formula: 1 1 2 1 v u R f + = = X-coordinate of center of Curvature and focus of concave mirror are negative and those for convex mirror are positive. In case of mirrors since light rays reflect back in X-direction, therefore -ve sign of v indicates real image and +ve sign of v indicates virtual image. (ii) Lateral magnification (or transverse magnification) denoted by m is defined as m = 2 1 h h and is related as m = v u − . From the definition of m positive sign of m indicates erect image and negative sign indicates inverted image. (iii) In case of successive reflection from mirrors, the overall lateral magnification is given by m1 × m2 × m3 ......, where m1, m2 etc. are lateral magnifications produced by individual mirrors. h1 and h2 denote the y coordinate of object and image respectively. Refraction Of Light When the light changes its medium some changes occurs in its properties the phenomenon is known as refraction. If the light is incident at an angle (0 < i < 90) then it deviates from its actual path. It is due to change in speed of light as light passes from one medium to another medium. If the light is incident normally then it goes to the second medium without bending, but still it is called refraction. Refractive index of a medium is defined as the factor by which speed of light reduces as compared to the speed of light in vacuum. c v = = speed of light in vacuum speed of light in medium . More (less) refractive index implies less (more) speed of light in that medium, which therefore is called denser (rarer) medium. Laws Of Refraction (a) The incident ray, the normal to any refracting surface at the point of incidence and the refracted ray all lie in the same plane called the plane of incidence or plane of refraction. (b) Sin i Sin r = Constant for any pair of media and for light of a given wave length. This is known as Snell's Law. Also, Sini Sinr = 2 1 n n = 1 2 v v = 1 2   For applying in problems remember n1sini = n2sinr 2 1 n n = 1n2 = Refractive Index of the second medium with respect to the first medium.  This sign convention is used for reflection from mirror, refraction through flat or curved surfaces or lens. Note Q. Match the corresponding entries of Column 1 with Column 2. [Where m is the magnification produced by the mirror] Column 1 Column 2 (A) m = – 2 (p) Convex mirror (B) m = − 1 2 (q) Concave mirror (C) m = +2 (r) Real image (D) m = + 1 2 (s) Virtual image Sol. Magnification in the mirror, m = − v u m = −2 ⇒ v = 2u As v and u have same signs so the mirror is concave and image formed is real. m = − 1 2 ⇒ v = u 2 ⇒ Concave mirror and real image. m = +2 ⇒ v = −2u As v and u have different signs but magnification is 2 so the mirror is concave and image formed is virtual. m = + 1 2 ⇒ v = − u 2 As v and u have different signs with magnification ( 1 2 ) so the mirror is convex and image formed is virtual. A → q and r; B→ q and r; C → q and s; D → p and s