LIGHT AND GEOMETERIC OPTICS ATWOOD S MACHINE. 700 nm Wavelength, λ. Frequency, f

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1 LIGHT AND GEOMETERI OPTIS ATWOOD S MAHINE 1. ELETROMAGNETI WAVES White light is a mixture of all visible colors. When a beam of white light passes through a glass prism, the resulting beam is dispersed into a spectrum of colors. Dispersion of light in a transparent material occurs because the index of refraction of the material varies with wavelength, with higher indices corresponding to shorter wavelengths. Wavelengths in the narrow, visible light spectrum range from 750 nm for the color red down to 400 nm for the color violet as shown below. 700 nm Wavelength, λ 400 nm 4x10 14 Hz requency, f 7.5x10 14 Hz However, visible light makes up just a tiny portion of the large electromagnetic spectrum. Typef waves with longer wavelengths than visible light include infrared radiation, microwaves, and radio waves. Those with shorter wavelengths include ultraviolet radiation, x-rays, and gamma-rays. ELETROMAGNETI WAVES λ (m) f (Hz) radio waves x10 5-9x10 8 Hz microwaves 1x x10 9-3x10 11 Hz infrared radiation (IR) 7x x10-3 3x x10 14 Hz visible light (VIS) 4x x10-7 4x x10 14 Hz ultraviolet (UV) 1x x x x10 16 Hz x-rays 1x x10-8 4x x10 19 Hz gamma-rays < 1x10-11 > 3x10 19 Hz Because light is made up of transverse waves, it can be polarized. The direction of polarization is taken to be the direction of the electric field vector. A special filter known as a polarizer produces polarized light from unpolarized light. The same filter can be used as an analyzer to determine whether or not light is polarized. When the axif the analyzer is parallel to the plane of polarized light, the greatest amount of light is transmitted. When the analyzer is perpendicular to the plane of polarized light, no light transmission occurs. 2. RELETION & RERATION

2 KEY ONEPT LIGHT & GEOMETERI OPTIS Light is assumed to travel along straight-line paths known as rays. When light strikes a surface, some of it undergoes reflection. A light ray strikes a surface at a certain angle of incidence, θ i relative to the surface normal, and is reflected at an identical angle of reflection, θ r. This is the law of reflection as given by: θ i = θ r θ i θ r If the surface of reflection is a flat, shiny mirror, the process is known as specular reflection. The law also holds for diffuse reflection from a rough surface as long as each small section of surface is considered separately. If a light ray passes into a transparent medium at an angle θ 1 that is not equal to 90, the path of the ray bends. This bending of light is known as refraction, and the angle θ 2 at which it is bent is known as the angle of refraction. θ 1 θ 2 Light travels at a speed of c = m/s in a vacuum, but travels slower in other transparent media such as water or glass. It is the wavelength of light, not the frequency, that varies from medium to medium. The index of refraction n is the ratio of the speed of light in a vacuum c to the speed of light in another medium v as given by: n = c v The index of refraction can never be less than one because v can never be greater than c. When light passes from one medium to another medium, the angle of refraction θ 2 dependn the angle of incidence θ 1 and the speed of light in the two media involved. Therefore, the index of refraction in first medium n 1 is related to that in the second medium n 2 by the equation: n 1 sinθ 1 = n 2 sinθ 2 This relationship is known as Snell s Law. If light rays traveling in a medium with a high index of refraction strike a second medium with a lower index of refraction at an angle that is large enough, the rays cannot

3 KEY ONEPT LIGHT & GEOMETERI OPTIS refract into the second medium, and all of the rays are reflected at the interface. This phenomenon is known as total internal reflection. The angle at which it occurs is given by: sinθ = n 2 n 1 where the angle θ c is known as the critical angle. 2. MIRRORS & LENSES When looking at a plane mirror, the image appears to be located behind the mirror. Because light rays do not actually pass through this image, it is known as a virtual image. In the case of a plane mirror, the image distance s i from the mirror is the same as the object distance from the mirror. The most common curved mirror is a spherical mirror. A concave or converging mirror has its reflecting surface on the inside of the sphere. Parallel light rays reflecting on a converging mirror converge to a focal point which is located midway between the mirror and its center of curvature. Therefore, the focal length f of the mirror is half the radiuf curvature R. A convex or diverging mirror has its reflecting surface on the outside of the sphere. Parallel light rays that are reflected by a diverging lens diverge as if their origin were a focal point behind the mirror. onverging Mirror Diverging Mirror There are certain principle rays that are defined according to their path with respect to the mirror s geometry. These include: A parallel ray that is incident along a path parallel to the mirror s axis and is reflected through the focal point. A chief ray that is incident through the center of curvature and is reflected back along its incident path. A focal ray that passes through the focal point and is reflected parallel to the mirror s axis. Parallel ray hief ray ocal ray

4 KEY ONEPT LIGHT & GEOMETERI OPTIS The image formed by a converging mirror can be real or virtual, whereas the image formed by a diverging mirror can only be virtual. The image characteristics depend on the position of the object relative to the mirror. or a converging mirror these characteristics can be summarized as follows: or > R the image is real, inverted, and reduced. or = R the image is real, inverted, and the same size. or R > > f the image is real, inverted, and enlarged. or = f the image is at infinity. or < f the image is virtual, upright, and enlarged. f object image real Inverted enlarged R s i The object distance, the image distance, and the focal length are related by the spherical mirror equation: = 1 s i f and the magnification M of the mirror is given by: M = s i = h i h o where h i is the image height and h o is the object height. A lens is a piece of curved, clear material that bends light by refraction. A biconvex spherical lens is a converging lens with both surfaces convex. A biconcave spherical lens is a diverging lens with both surfaces concave. These lenses have two focal points and two centerf curvature, one for each lens surface.

5 KEY ONEPT LIGHT & GEOMETERI OPTIS onverging lens Diverging lens A converging lens can form either a real or a virtual image, whereas a diverging lens is capable of forming only a virtual image. The image characteristics depend on the position of the object relative to the lens. or a converging lens these characteristics can be summarized as follows: or > f the image is real and inverted, and it can be enlarged, reduced, or the same size. or = f the image converges at infinity. or < f the image is virtual, upright, and enlarged. h o object image real inverted reduced h i s i The object distance, the image distance, and the focal length are related by the lens equation: = 1 s i f and the magnification M of the lens is given by: M = s i = h i h o 4. DIRATION When waves encounter an object, they bend around its edge into the region directly behind the region. This phenomenon is known as diffraction. Diffraction occurs at the

6 KEY ONEPT LIGHT & GEOMETERI OPTIS edgef openingr slits. The diffraction effect is greatest when the slit width in the order of the wavelength of light that is being diffracted. In Young s double-slit experiment, light emerging from the two slits is used as two coherent sources. When the light is projected onto a screen, an interference pattern appears that consistf a serief alternating bright and dark fringes around a central maximum. Because the bright fringes indicate constructive interference, the path difference between two waves must be an integral number of wavelengths. The positions of the bright fringes are given by the equation: dsinθ = mλ m = 0,1,2,3,... where d is the distance between slits, θ is the angle of the bright fringe from the center line, λ is the wavelength of the illuminating light and m is the order number. Dark fringeccur when the path difference is an odd number of half wavelengths, and their positions are given by the equation: dsinθ = m( λ 2) m =1,3,5,... or a single slit, the width of the central maximum of the diffraction pattern is twice that of the side fringes. The positionf the dark side fringes are given by the equation: wsinθ = mλ m =1,2,3,... where w is the slit width. A diffraction grating is a device that consistf thousandf slits per centimeter. The conditions required for a diffraction grating to produce bright fringes are the same as for the double-slit setup. Diffraction gratings produce very sharp bright lines and are used in spectrometers to make precise measurementf light wavelengths. When light reflectff the two surfacef a thin film, an interference pattern is formed. This phenomenon is known as thin film interference. A thin coating is applied to lenses to make them nonreflective. or the coating to be nonreflective to light of wavelength λ, the minimum thickness t of the coating is given by the equation: t = λ 4n where n is the refractive index of the lens glass. When a curved lens is placed on a flat glass plate, the wedge of air that is trapped between the two produces an interference pattern consisting of concentric bright and dark circular fringes known as Newton s rings.