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2054Lecture15

# 2054Lecture15 - Formation of Images Topics of Discussion...

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Unformatted text preview: Formation of Images Topics of Discussion Flat Mirrors Spherical Mirrors Ray Tracing for Mirrors The Mirror Equation & Conventions Images Formed by Refraction Ray Tracing for Lens The Lens Equation & Conventions The Lens Maker's Equation Flat Mirrors The object and image distance of a flat mirror are equal. The magnification M of a flat mirror is unity, that is M=1. The image of a flat mirror is unmagnified, virtual and upright. Spherical Mirrors Spherical mirrors are either concave or convex with a radius of curvature R. Convex mirrors always form virtual images while concave may be either real or virtual. The magnification M is given by M = q / p = h' / h, where p and q are the object and image distances, and h and h' are the object and image heights. Ray Tracing Ray tracing is a method for drawing the propagation of light through an optical system. We can locate an image & determine its characteristics by using two of the three types of rays: the parallel ray, the chief ray and the focal ray. Ray Tracing for Mirrors A parallel ray is a ray that is incident along a path parallel to the principal axis reflected through (or appears to go through) the focal point of a spherical mirror. A chief ray is a ray that is incident through the center of curvature of a spherical mirror. A focal ray is a ray that passes through (or appears to go through) the focal point and is reflected parallel to the principal axis of the spherical mirror. The Mirror Equation The mirror equation of a spherical mirror of curvature R is given by 1 1 2 + = p q R . The focal length f of a spherical mirror is given by f = R / 2. Conventions for Spherical Mirrors A positive sign is given to the focal length of a concave mirror, a object distance in front of the mirror (real object), an image distance in front of the mirror (real image) and a magnification that is upright with respect to the object. A negative sign is given to the focal length of a convex mirror, a object distance behind the mirror (virtual object), an image distance behind the mirror (virtual image) and a magnification that is inverted with respect to the object. Images Formed by Refraction Equations for Flat Surfaces (n1 > n2): n1/ p = n2/ q Equations for Spherical Surfaces (n2 > n1): M = n1q / n2p = h' / h n1 n 2 n 2 - n1 + = p q R Ray Tracing for Lens A parallel ray is a ray that is incident along a path parallel to the principal axis and after refraction either passes through the focal point on the image side of a converging lens or appears to diverge through from the focal point on the object side of a diverging lens. A chief ray is a ray that passes through the center of curvature of a lens and undeviated. A focal ray is a ray that passes through the focal point on the object side of a converging lens or appears to pass through the focal point on the image side of a diverging lens, and after refraction, is parallel to the lens's principal axis. Thin Lenses Lenses are either convex or concave. The focal length f is the image distance that corresponds to an infinite object distance. The Thin Lens Equation: 1 1 1 + = p q f Thin Lens Conventions A positive sign is given to the focal length of a converging lens, a object distance is to the left of the lens (real object), an image distance to the right of the lens (real image) and a magnification that is upright with respect to the object. A negative sign is given to the focal length of a diverging lens, a object distance is to the right of the lens (virtual object), an image distance is to the left of the lens (virtual image) and a magnification that is inverted with respect to the object. Lens Maker's Equation Let R1 and R2 be the radius of curvature for the front and back surfaces of a lens and n is the index of refraction of the material. Then the lens maker's equation is given by 1 1 1 ( n - 1) + = . R1 R2 f ...
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