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Ex. 1 - What is the minimum mirror height necessary for a person to see their full image?

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## Ex. 1 - What is the minimum mirror height necessary for a person to see their full image?

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**A wave front consists of all points in a wave that are in**the same phase of motion. A wave front is one of many properties that light waves share with sound waves.**A radial line pointing outward from a light source and**perpendicular to the wave front is called a ray. Rays point in the direction of the velocity of the wave.**Waves whose wave fronts are flat surfaces are called plane**waves. The rays for a plane wave are parallel to each other. A ray is a narrow beam of light.**The law of reflection states that the incident ray, the**reflected ray, and the normal all lie in the same plane, and the angle of reflection θr equals the angle of incidence θi: θr = θi.**When light rays strike a smooth surface, reflected rays are**parallel (as in a mirror), this is called specular reflection. Light is reflected in various directions when it strikes an irregular surface, this is called diffuse reflection.**Properties of the image in a plane mirror:1. upright**(erect)2. same size3. same distance into mirror as object’s distance from mirror.**The rays that we see reflected from a plane mirror seem to**emanate from a point behind the mirror. The rays cannot really originate there so the image is called a virtual image.**Curved mirrors can produce images from which the light rays**actually emanate. These are called real images.**Ex. 1 - What is the minimum mirror height necessary for a**person to see their full image?**There are two types of spherical mirrors: concave and**convex.**Center of curvature, C, is the center of the original**sphere.Vertex, V, is the center of the mirror.**Principle axis of the mirror is the line drawn through C and**V.Secondary axis is any other line drawn through C to the mirror.Normal is a radius from the point of incidence of a light ray.**Focal Point F of the mirror is the point on the PA where**light rays close to and parallel to the PA converge.For a curved mirror, the focal point is one-half the distance to the center of curvature, one-half the radius of the sphere f = R/2, if the curvature of the mirror is gradual.**Focal length, f, is the distance from the vertex to the**principle focus.Rays that lie close to the principle axis are paraxial rays(paraxial rays lie close to the principle axis, but are not necessarily parallel to it), f = R/2 is only valid for paraxial rays.**Rays that are far from the principle axis do not converge to**a single point after reflection. The resulting image is blurred; this is called spherical aberration. It can be minimized by using a mirror with a small curvature (small diameter compared to radius of curvature).**A parabolic mirror has no spherical aberration, even if it**is a large mirror.**Convex mirrors also have focal points with focal lengths**that are one-half the radius of curvature. We assign the focal length of convex mirror a negative value: f = -R/2.**The image formed in a curved mirror can be produced by ray**tracing.**It is convenient to produce three rays that leave the same**point on an object:Ray 1 is parallel to the principle axis and reflects through the focal point,Ray 2 passes through the focal point and reflects parallel to the principle axis,Ray 3 travels through the center of curvature and thus reflects back on itself.**Images formed by concave mirror:Case #1 Object at an**infinite distance.**Case #2 Object at a finite distance beyond the center of**curvature**Case #4 Object between the center of curvature and principle**focus**1. The numerical value of the focal length f of a concave**mirror is positive.2. The numerical value of the focal length f of a convex mirror is negative.**3. The numerical value of the real object distance do is**positive.4. The numerical value of the real image distance di is positive.5. The numerical value of the virtual image distance di is negative.**Ex. 3 - A 2.0-cm-high object is placed 7.10 cm from a**concave mirror whose radius of curvature is 10.20 cm. Find (a) the location of the image and (b) its size.**Ex. 4 - An object is placed 6.00 cm in front of a concave**mirror that has a 10.0-cm focal length. (a) Determine the location of the image. (b) If the object is 1.2 cm high, find the image height.**Ex. 5 - A convex mirror is used to reflect light from an**object placed 66 cm in front of the mirror. The focal length of the mirror is f = -46 cm. Find (a) the location of the image and (b) the magnification.**Ex. 6 - An object is placed 9.00 cm in front of a mirror.**The image is 3.00 cm closer to the mirror when the mirror is convex than when it is planar. Find the focal length of the convex mirror.