Geometric Optics-1 (2).pdf - Geometric Optics 1 Wave Fronts and Rays Point source A wave front is a surface passing through points of a wave that have

# Geometric Optics-1 (2).pdf - Geometric Optics 1 Wave Fronts...

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Unformatted text preview: Geometric Optics 1 Wave Fronts and Rays Point source • A wave front is a surface passing through points of a wave that have the same phase and amplitude Geometric Optics – The Ray Approximation • Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media • The ray approximation is used to represent beams of light • A ray of light is an imaginary line drawn along the direction of travel of the light beams • The rays, corresponding to the direction of the wave motion, are perpendicular to the wave fronts 2 The 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. LAWS OF REFLECTION: 1.The incident ray, the reflected ray, and the normal to the surface all lie in the same plane 2.The angle of reflection is equal to the angle of incidence θ1 = θ 1 ’ 3 The Reflection of Light 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 Diffuse reflection is reflection from a rough surface The reflected rays travel in a variety of directions Diffuse reflection makes the dry road easy to see at night 4 Images Formed of by a Plane Mirror • Simplest possible mirror Ray diagram = a geometric construction to locate the image of an object formed by a mirror or lens. • it is necessary to trace at least two rays of light as they reflect from the mirror 1. One ray is incident perpendicular on the mirror follows path PQ and reflects back on itself 2. A second ray follows path PR and reflects according to the Law of Reflection 5 Images Formed of by a Plane Mirror Types of Images for Mirrors and Lenses A real image is one in which light actually passes through the image point • It is formed at the intersection of real rays • Real images can be displayed on screens A virtual image is one in which the light does not pass through the image point • The image is formed at the intersection of extensions of rays. • Virtual images cannot be displayed on screens 6 The Refraction of Light Looking at the fish tank as shown, we can see the same fish in two different locations, because light changes directions when it passes from water to air. In this case, the light can reach the observer by two different paths, and so the fish seems to be in two different places. This bending of light is called refraction and is responsible for many optical phenomena. When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium The ray that enters the second medium is bent at the boundary • This bending of the ray is called refraction. 7 The Refraction of Light • The change in direction of a light ray depends on how the speed of light changes when it crosses from one medium to another. The speed of light is greater in medium 1 than in medium 2 in the situations shown here. (a) A ray of light moves closer to the perpendicular when it slows down. This is analogous to what happens when a lawn mower goes from a footpath to grass. (b) A ray of light moves away from the perpendicular when it speeds up. This is analogous to what happens when a lawn mower goes from grass to footpath. The paths are exactly reversible. 8 The Index of Refraction Light travels through a vacuum at a speed c 3.00 108 m s Light travels through materials at a speed less than its speed in a vacuum. The index of refraction of a material is the ratio of the speed of light in a vacuum to the speed of light in the material: Speedof light in vacuum c n Speedof light in the material v The speed of light in materials: vλf • The frequency of the electromagnetic waves stays always the same, it does not depend on material the wave travels through. • The speed of light changes when light travels through different materials because the wavelength changes (the frequency remains constant) 9 The Refraction of Light SNELL’S LAW OF REFRACTION When light travels from a material with one index of refraction to a material with a different index of refraction, the angle of incidence is related to the angle of refraction by n1 sinθ1 n 2 sinθ2 10 The Refraction of Light When light refracts into a material where its speed is lower (index of refraction higher n2>n1) • The angle of refraction is less than the angle of incidence • The ray bends toward the normal When light refracts into a material where its speed is higher (index of refraction lower n2<n1) • The angle of refraction is greater than the angle of incidence • The ray bends away from the normal 11 The Refraction of Light Example: Determining Index of Refraction from Refraction Data Find the index of refraction for medium 2 in the figure assuming medium 1 is air and given that the angle of incidence is 300 and the angle of refraction is 220. θ1 30 θ 2 220 medium 1 is air : n1 1 n2 ? n1 sinθ1 n 2 sinθ2 n1 sinθ1 1.00 sin 30 n2 sin θ 2 sin 22 n 2 1.33 12 Total Internal Reflection Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction When light passes from a medium of larger refractive index into one of smaller refractive index, the refracted ray bends away from the normal. A particular angle of incidence will result in an angle of refraction of 90° • This angle of incidence is called the critical angle θc. For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary. n 2 sinθ 2 n 2 sin 900 n1 sinθ1 n 2 sinθ 2 sinθ1 sinθc n1 n1 Critical angle sinθc n2 n1 n1 n 2 13 Dispersion of Light • The index of refraction of a transparent medium depends on the wavelength of the light vλf n Speedof light in vacuum c Speedof light in the material v n λ vacuum f λ medium f n λ vacuum λ medium • This dependence of n on λ is called dispersion White light is dispersed by the prism (shown exaggerated): • Since the index of refraction varies with wavelength, the angles of refraction vary with wavelength. • A sequence of red to violet is produced, because the index of refraction increases steadily with decreasing wavelength. 14 Dispersion of Light Light rays corresponding to different colors bend by different amounts. 15 Image Formation by Lenses A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane Lenses are commonly used to form images by refraction in optical instruments These are examples of converging lenses • They have positive focal lengths • They are thickest in the middle • These are examples of diverging lenses • They have negative focal lengths • They are thickest at the edges 16 Image Formation by Lenses The focal length, ƒ, is the image distance that corresponds to an infinite object distance A thin lens has two focal points, corresponding to parallel rays from the left and from the right • A thin lens: the distance between the surface of the lens and the center of the lens is negligible Focal Length of a Converging Lens f > 0 The parallel rays pass through the lens and converge at the focal point The parallel rays can come from the left or right of the lens. Focal Length of a Diverging Lens f <0 The parallel rays diverge after passing through the diverging lens The focal point is the point where the rays appear to have originated 17 Image Formation by Lenses RAY DIAGRAMS Ray diagrams - used to trace image formation Two rays are drawn • The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal points • The second ray is drawn through the center of the lens and continues in a straight line There are an infinite number of rays, these are convenient 18 Notation for Mirrors and Lenses The object distance = distance from the object to the mirror or lens • Denoted by do The image distance = distance from the image to the mirror or lens • Images are formed at the point where rays actually intersect or appear to originate • Denoted by di • The lateral magnification of the mirror or lens is the ratio of the image height to the object height • Denoted by m image height h i m object height ho 19 The Thin-Lens Equation and Magnification The lens equation : 1 1 1 do di f The magnification : image height h i d m i object height h o do The equations can be used for both converging and diverging lenses • A converging lens has a positive focal length • A diverging lens has a negative focal length 20 IMAGE FORMATION BY A CONVERGING LENS 1. Object placed further than twice the focal length from the lens: the image is real, inverted and smaller than the object. 2. Object placed between F and 2F: the image is real, inverted and larger than the object. 3. Object placed between F and the lens, the image is virtual, upright and larger than the object. 21 IMAGE FORMATION BY A DIVERGING LENS A diverging lens always forms a virtual image, upright and smaller than the object. 22 The Thin-Lens Equation and Magnification Example: The Real Image Formed by a Camera Lens A 1.70-m tall person is standing 2.50 m in front of a camera. The camera uses a converging lens whose focal length is 0.0500 m. (a) Find the image distance and determine whether the image is real or virtual. (b) Find the magnification and height of the image on the film. h 1.70 m p 2.50 m f 0.05 m a) q ? b) M ? h' ? The lens equation : 1 1 1 do di f The magnification : image height h i d m i object height h o do h o 1.70 m d o 2.50 m f 0.05 m a) d i ? b) m ? hi ? 23 The Thin-Lens Equation and Magnification Example: The Real Image Formed by a Camera Lens h o 1.70 m d o 2.50 m f 0.05 m a) d i ? b) m ? hi ? (a) 1 1 1 do di f (b) m di do 1 1 1 di f do 1 1 1 d i 0.0500 m 2.50 m m m 0.0204 d i 0.051 m di > 0 real image 0.0510 m 2.50 m m < 0 image inverted m 1 The image is smaller than the object m hi ho h i m h o 0.02042.50 m h i 0.0347 m 24 Image Formation by Mirrors Flat Mirror The person’s right hand becomes the image’s left hand. The image is as far behind the mirror as the object is in front • di = do The image is unmagnified = the image height is the same as the object height • hi = ho and m = 1 The image is virtual The image is upright - It has the same orientation as the object There is an apparent left-right reversal in the image 25 Spherical Mirrors If the inside surface of the spherical mirror is polished, it is a concave mirror. If the outside surface is polished, is it a convex mirror. The law of reflection applies, just as it does for a plane mirror. The principal axis of the mirror is a straight line drawn through the center of curvature and the midpoint of the mirror. 26 Spherical Mirrors - Concave Mirrors • • • • R= the radius of curvature C = the center of curvature V = the center of the spherical segment The principle axis of the mirror = a line drawn from C to V • For concave mirrors: f >0 Focal Length •Incident parallel rays are reflected through the focal point F •focal length (f)= the distance from the mirror to the focal point The focal point of a concave mirror is halfway between the center of curvature of the mirror C and the mirror at V f 12 R V 27 Spherical Mirrors - Concave Mirrors Rays that lie close to the principal axis are called paraxial rays. Rays that are far from the principal axis do not converge to a single point. The fact that a spherical mirror does not bring all parallel rays to a single point is known as spherical aberration. 28 Spherical Mirrors Image Formed by a Concave Mirror The mirror equation : 1 1 2 R f do di R 2 1 1 1 do di f The magnification of the image: m image height h i d i object height h o do • hi is negative when the image is inverted with respect to the object 29 Spherical Mirrors Image Formed by a Concave Mirror Example A concave mirror has a focal length of 10.0 cm. An object is placed at 25 cm in front of the mirror. a. What is the location of the image? b. What is its magnification? c. Is the image real or virtual, inverted or upright, larger or smaller? d. Draw a ray diagram. 30 Spherical Mirrors Image Formed by a Concave Mirror f 10 cm; d o 25 cm a) d i ? 1 1 1 do di f 1 1 1 1 1 d i f d o 10 cm 25 cm d i 16.7 cm The mirror equation : 1 1 2 R f do di R 2 1 1 1 do di f m hi d i ho do The image is real (di>0). b) m di do m 16.7 cm 25 cm m - 0.668 m < 0 The image is inverted m 1 The image is smaller than the object 31 Spherical Mirrors - Convex Mirrors When paraxial light rays that are parallel to the principal axis strike a convex mirror, the rays appear to originate from the focal point. f 12 R 32 ...
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• Summer '11
• Stanischevsky
• Light, Total internal reflection, Geometrical optics, rays
• • •  