Optics. a- Before the beginning of the nineteenth century, light was considered to be a stream of particles.

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1 Optics 1- Light Nature: a- Before the beginning of the nineteenth century, light was considered to be a stream of particles. The particles were either emitted by the object being viewed or emanated from the eyes of the viewer. Newton was the chief architect of the particle theory of light. He believed the particles left the object and stimulated the sense of sight upon entering the eyes. b- Christian Huygens argued that light might be some sort of a wave motion. Thomas Young (in 1801) provided the first clear demonstration of the wave nature of light. He showed that light rays interfere with each other. Such behavior could not be explained by particles. c- In view of these developments, light must be regarded as having a dual nature. Light exhibits the characteristics of a wave in some situations and the characteristics of a particle in other situations. This chapter investigates the wave nature of light. λ = h/p Where λ is the wavelength, h is Planck s constant, and P is the momentum

2 2- The electromagnetic spectrum - The electromagnetic spectrum is a continuum of all electromagnetic waves arranged according to frequency and wavelength. - The sun, earth, and other bodies radiate electromagnetic energy of varying wavelengths. - Electromagnetic energy passes through space at the speed of light in the form of sinusoidal waves. 3- Measurements of the Speed of Light Fizeau s Method. This was the first successful method for measuring the speed of light by means of a purely terrestrial technique. It was developed in 1849 by Armand Fizeau. He used a rotating toothed wheel. The distance between the wheel (considered to be the source) and a mirror was known.

3 d is the distance between the wheel and the mirror. Δt is the time for one round trip. Then Fizeau found a value of c = 3.1 x 10 8 m/s. 4- Reflection of Light - A ray of light, the incident ray, travels in a medium. - When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium. - This means it is directed backward into the first medium. - For light waves traveling in three-dimensional space, the reflected light can be in directions different from the direction of the incident rays.

4 - There are two types of reflection: a- Specular reflection is reflection from a smooth surface. The reflected rays are parallel to each other. All reflection in this text is assumed to be specular. b- Diffuse reflection is reflection from a rough surface. The reflected rays travel in a variety of directions. A surface behaves as a smooth surface as long as the surface variations are much smaller than the wavelength of the light. Law of Reflection - The normal is a line perpendicular to the surface. - It is at the point where the incident ray strikes the surface. - The incident ray makes an angle of θ 1 with the normal. - The reflected ray makes an angle of θ 1 with the normal. - The angle of reflection is equal to the angle of incidence. - θ 1 = θ 1 - This relationship is called the Law of Reflection.

5 - The incident ray, the reflected ray and the normal are all in the same plane. - Because this situation happens often, an analysis model, wave under reflection, is identified. - Notation note: - The subscript 1 refers to parameters for the light in the first medium. - If light travels in another medium, the subscript 2 will be associated with the new medium. - - Ex: In the following Figure, find the angle of reflection at the surface M 2.

6 5- Refraction of Light - When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the energy is reflected and part enters the second medium. - The ray that enters the second medium changes its direction of propagation at the boundary. - This bending of the ray is called refraction. - The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane. - The angle of refraction depends upon the material and the angle of incidence. - v 1 is the speed of the light in the first medium and v 2 is its speed in the second medium. - The path of the light through the refracting surface is reversible. - For example, a ray travels from A to B. - If the ray originated at B, it would follow the line AB to reach point - A. sin sin θ θ v v Note: - Light may refract into a material where its speed is lower. - The angle of refraction is less than the angle of incidence. - The ray bends toward the -

7 normal. - Light may refract into a material where its speed is higher. - - The angle of refraction is greater than the angle of incidence. - The ray bends away from the normal Light in a Medium - The light enters from the left. - The light may encounter an electron. - The electron may absorb the light, oscillate, and reradiate the light. - The absorption and radiation cause the average speed of the light moving through the material to decrease. - The Index of Refraction: - The speed of light in any material is less than its speed in vacuum. - The index of refraction, n, of a medium can be defined as speed of light in a vacuum c n speed of light in a medium v For a vacuum, n = 1 We assume n = 1 for air also For other media, n > 1 n is a dimensionless number greater than unity. n is not necessarily an integer.

8 As light travels from one medium to another, its frequency does not change. Both the wave speed and the wavelength do change. The wavefronts do not pile up, nor are they created or destroyed at the boundary, so the frequency ƒ must stay the same. The frequency stays the same as the wave travels from one medium to the other. v = ƒλ ƒ 1 = ƒ 2 but v 1 v 2 so λ 1 λ 2 The ratio of the indices of refraction of the two media can be expressed as various ratios. c λ v n n λ v c n n The index of refraction is inversely proportional to the wave speed. As the wave speed decreases, the index of refraction increases. The higher the index of refraction, the more it slows downs the light wave speed.

9 The previous relationship can be simplified to compare wavelengths and indices: λ 1 n 1 = λ 2 n 2 In air, n 1 = 1 and the index of refraction of the material can be defined in terms of the wavelengths. λ λin vacuum n λn λin a medium - Snell s Law of Refraction: n 1 sin θ 1 = n 2 sin θ 2 θ 1 is the angle of incidence θ 2 is the angle of refraction The experimental discovery of this relationship is usually credited to Willebrord Snell and is therefore known as Snell s law of refraction.

10 Example: A beam of light traveling in air is incident on a slab of transparent material. The incident beam makes an angle of 40.0 with the normal, and the refracted beam makes an angle of 26.0 with the normal. Find the index of refraction of the material. Solution: Critical angle: The maximum possible angle of refraction is 90-degrees. If you think about it (a practice that always helps), you recognize that if the angle of refraction were greater than 90 degrees, then the refracted ray would lie on the incident side of the medium - that's just not possible. So in the case

11 of the laser beam in the water, there is some specific value for the angle of incidence (we'll call it the critical angle) that yields an angle of refraction of 90-degrees. - Total Internal Reflection: Total internal reflection (TIR) is the phenomenon that involves the reflection of all the incident light off the boundary. TIR only takes place when both of the following two conditions are met: the light is in the more dense medium and approaching the less dense medium. the angle of incidence is greater than the so-called critical angle. Total internal reflection will not take place unless the incident light is traveling within the more optically dense medium towards the less optically dense medium. TIR will happen for light traveling from water towards air, but it will not happen for light traveling from air towards water. TIR would happen for light traveling from water towards air, but it will not happen for light traveling from water (n=1.333) towards crown glass (n=1.52). TIR occurs because the angle of refraction reaches a 90-degree angle before the angle of incidence reaches a 90-degree angle. - Fiber Optics - An application of internal reflection - Plastic or glass rods are used to pipe light from one place to another. - Applications include:

12 Medical examination of internal organs Telecommunications Construction of an Optical Fiber: The transparent core is surrounded by cladding. The cladding has a lower n than the core. This allows the light in the core to experience total internal reflection. The combination is surrounded by the jacket.

13 Definition in mirrors and lenses 7- Mirrors and lenses Principal axis: The principal axis is a line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror. Center of Curvature: The point in the center of sphere from which the mirror was sliced is known as the center of curvature C Vertex: The point on the mirror's surface where the principal axis meets the mirror is known as the vertex,a The vertex is the geometric center of the mirror. Focal Point: Midway between the vertex and the center of curvature is a point known as the focal point; F. Radius of Curvature:

14 The distance from the vertex to the center of curvature is known as the radius of curvature, R. The radius of curvature is the radius of the sphere from which the mirror was cut. Focal Length: the distance from the mirror to the focal point is known as the focal length f. the focal length would be one-half the radius of curvature. Sign (rules) conventions for Mirrors Object distance is + if the object is in front of the mirror (real object). Object distance is - if the object is in back of the mirror (virtual object). Image distance is + if the image is in front of the mirror (real image). Image distance is - if the image is in back of the mirror (virtual image). Both F and R are + if the center of curvature is in front of the mirror (concave mirror). Both F and R are - if the center of curvature is in back of the mirror (convex mirror).

15 - Forming images with a plan mirror - The image formed by a plane mirror has the following properties: - 1. The image is as far behind the mirror as the object is in front The image is unmagnified, virtual, and erect. - Images Formed by Spherical Mirrors a- Concave Mirrors - A spherical mirror, has the shape of a section of a sphere. - This type of mirror focuses incoming parallel rays to a point. - In a concave mirror the light is reflected from the inner. Concave Mirrors forms a real image

16 b- Images Formed by Convex Mirrors (diverging mirror ) - The light is reflected from the outer, convex surface. - The image formed by convex mirror for a real object is virtual and upright and smaller than the object. - This type of mirror is often used in stores to foil shoplifters. - A single mirror can be used to survey a large field of view because it forms a smaller image of the interior of the store. - Ray tracing: - A- Ray tracing for concave mirror -

17 - Ray 1 is drawn from the top of the object parallel to the principal axis and is reflected through the focal point F. - Ray 2 is drawn from the top of the object through the focal point and is reflected parallel to the principal axis. - Ray 3 is drawn from the top of the object through the center of curvature C and is reflected back on itself. - B- Ray tracing for convex mirror - - Ray 1 is drawn parallel to the principal axis and is reflected away from the focal point F. - Ray 2 is drawn toward the focal point on the back side of the mirror and is reflected parallel to the principal axis. - Ray 3 is drawn toward the center of curvature C on the back side of the mirror and is reflected back on itself. - ============================================= - The mirror equation - Mirror equation in terms of radius of curvature

18 Mirror equation in terms of focal length The magnification of the image is Example: Assume that a certain concave spherical mirror has a focal length of 10.0 cm. Locate the image for an object distance of 5 cm and describe the image s characteristics. 1 f d i 1 do 1 d i d i d i = -10 cm di M 5 M = 2x Characteristics: VIRTUAL (opposite side) Enlarged Upright

19 8- Lenses - Sign Conventions for thin lenses: - - Object distance is + if the object is in front of the lens. - Object distance is - if the object is in back of the lens. - Image distance is + if the image is in back of the lens. - Image distance is - if the image is in front of the lens. - R1 and R2 are + if the center of curvature for each surface is in back of the lens. - R1 and R2 are - if the center of curvature for each surface is in front of the lens. - f is + for a converging lens. - f is - for a diverging lens. - Types of Lenses:

20 - Ray diagrams for thin lenses - A: Bi-convex lens. The first ray is drawn parallel to the principle axis. After being refracted by the lens, this ray passes through one of the focal points. The second ray is drawn through the center of the lens. This ray continuous in straight line. The third ray is drawn through the focal point, F, and emerges from the lens parallel to the principle axis. The image is real and inverted. -=-=-=-=-=-=-=-=-=-=-= B- Bi-Concave lens: The object is outside the front focal point of a diverging lens the image is virtual and erect.

21 Thin-lens equation: - The lens maker s equation: 1 f 1 ( n 1) R 1 1 R 2 Example: Find the focal length of a plano-convex lens, the radius of the curved surface being 10 cm, n= 1.5). [Ans: f=20 cm] The power of a lens is the measure of its ability to produce convergence of a parallel beam of light. The unit of power of a lens is measured is called a diopter (D). A convex lens of focal length 1 m has a power = + 1 diopter A convex lens of focal length 2 m has a power = diopter.

22 - law of refraction through lenses - A convex lens produces a real or virtual image depending on the location of the object. - Concave lens always produces virtual images of real objects.

23 First principal focal length f 1 = Second principal focal length, f 2 = =-=-=-=-=-=-==-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- =-=-=-=-=-=

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