Lecture 1-Optics and Light.pdf

Geometric Optics Introduction to Light Light is basic to almost all life on Earth. Light is a form of electromagnetic radiation. Light represents energy transfer from the source to the observer. Many phenomena depend on the properties of light. § Seeing a TV or computer monitor § Blue sky, colo...

Geometric Optics Introduction to Light Light is basic to almost all life on Earth. Light is a form of electromagnetic radiation. Light represents energy transfer from the source to the observer. Many phenomena depend on the properties of light. § Seeing a TV or computer monitor § Blue sky, colors at sunset and sunrise § Images in mirrors § Eyeglasses and contacts § Rainbows § Many others  The Ray Approximation in Ray Optics Ray optics (sometimes called geometric optics) involves the study of the propagation of light. It uses the assumption that light travels in a straight-line path in a uniform medium and changes its direction when it meets the surface of a different medium or if the optical properties of the medium are nonuniform. The ray approximation is used to represent beams of light. Ray Approximation The rays are straight lines perpendicular to the wave fronts. With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays. 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.  TYPES OFREFLECTION Specular Reflection Diffuse Reflection Diffuse reflection is reflection from a Specular reflection is reflection from a rough surface. smooth surface. The reflected rays travel in a variety of The reflected rays are parallel to each directions. other. A surface behaves as a smooth All reflection in this course is assumed surface as long as the surface to be specular. variations are much smaller than the wavelength of the light. Law of Reflection The angle of reflection is equal to the angle of incidence. θ1’= θ1 § This relationship is called the Law of Reflection. The incident ray, the reflected ray and the normal are all in the same plane. Multiple Reflections The incident ray strikes the first mirror. The reflected ray is directed toward the second mirror. There is a second reflection from the second mirror. Apply the Law of Reflection and some geometry to determine information about the rays. 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.  Refraction, cont. 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. § v1 is the speed of the light in the first medium and v2 is its speed in the second. Refraction Details, 1 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 normal. Refraction Details, 2 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 Note: c = 3.0 x 108 m/s Under normal circumstances, v 1 n is a dimensionless number greater than unity. § n is not necessarily an integer. Some Indices of Refraction Frequency Between Media 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 ƒ must stay the same. Index of Refraction Extended The frequency stays the same as the wave travels from one medium to the other. v = ƒλ (Wave Eqn.) § ƒ1 = ƒ2 but v1  v2 so λ1  λ2 The ratio of the indices of refraction of the two media can be expressed as various ratios. 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 down the light wave speed. More About Index of Refraction The previous relationship can be simplified to compare wavelengths and indices: λ1n1 = λ2n2 In air, n1 = 1 and the index of refraction of the material can be defined in terms of the wavelengths. Snell’s Law of Refraction n1 sin θ1 = n2 sin θ2 § θ1 is the angle of incidence § θ2 is the angle of refraction The experimental discovery of above relationship is usually credited to Willebrord Snell and is therefore known as Snell’s law of refraction. For light traveling from air into another medium of refractive index n, Snell’s law can be used to define n.  Problems 1. Light strikes a diamond (n = 2.42) at an angle of 60 relative to the normal to the surface. What is the angle of refraction? 2. Light is refracted through a diamond. If the angle of incidence is 30°, and the angle of refraction is 12o, what is the index of refraction of diamond? 3. The wavelength of the red light from a helium-neon laser is 633nm in air but 474 in the aqueous humor inside your eye-ball. Calculate: (a)the index of refraction of the aqueous humor , (b)the speed and frequency of the light in this substance. 4. Light strikes a diamond (n = 2.42) immersed in glycerin (n = 1.473) at an angle of 60° relative to the normal to the surface. What is the angle of refraction?  Prism A ray of single-wavelength light incident on the prism will emerge at angle d from its original direction of travel. § d is called the angle of deviation. § F is the apex angle or the angle of the prism. Assignment Look for the relationship between n, δ and Φ for a prism  Dispersion For a given material, the index of refraction varies with the wavelength of the light passing through the material. This dependence of n on λ is called dispersion. Snell’s law indicates light of different wavelengths is bent at different angles when incident on a refracting material. Refraction in a Prism Since all the colors have different angles of deviation, white light will spread out into a spectrum. § Violet deviates the most. § Red deviates the least. § The remaining colors are in between. The Rainbow A ray of light strikes a drop of water in the atmosphere. It undergoes both reflection and refraction. § First refraction at the front of the drop § Violet light will deviate the most. § Red light will deviate the least. Total Internal Reflection A phenomenon called total internal reflection can occur when light is directed from a medium having a given index of refraction toward one having a lower index of refraction. Critical Angle There is a particular angle of incidence that will result in an angle of refraction of 90°. § This angle of incidence is called the critical angle, θC. Critical Angle, cont. For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary. § This ray obeys the law of reflection at the boundary. Total internal reflection occurs only when light is directed from a medium of a given index of refraction toward a medium of lower index of refraction. Everyday Occurrences of Refraction Bending of stick placed in water Pool of water appears shallower than it truly is Other examples  Fiber Optics An application of internal reflection Plastic or glass rods are used to “pipe” light from one place to another. Applications include: § 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. Fiber Optics, cont. A flexible light pipe is called an optical fiber. A bundle of parallel fibers (shown) can be used to construct an optical transmission line.  Problems. 1. A diver shines an underwater searchlight at the surface of a pond (n = 1.33). At what angle (relative to the surface) will the light be totally reflected? 2. A layer of ethyl alcohol (n = 1.361) is on top of water (n = 1.333). To the nearest degree, at what angle relative to the normal to the interface of the two liquids is light totally reflected? 3. A layer of water (n = 1.333) floats on carbon tetrachloride (n = 1.461) contained in an aquarium. To the nearest degree, what is the critical angle at the interface between the two liquids?