Download
1 / 55
680 likes | 1.14k Vues
Geometric Optics. Mirrors, light, and image formation. Geometric Optics. Understanding images and image formation, ray model of light, laws of reflection and refraction, and some simple geometry and trigonometry The study of how light rays form images with optical instruments.
E N D
Geometric Optics Mirrors, light, and image formation
Geometric Optics • Understanding images and image formation, ray model of light, laws of reflection and refraction, and some simple geometry and trigonometry • The study of how light rays form images with optical instruments
Reflection and refraction on plane mirrors Reflection and Refraction at a plane Surface
Key terms • Anything from which light rays radiate • Object • Anything from which light rays radiate that has no physical extent • Point object • Real objects with length, width, and height • Extended objects
Image formation by a Plane mirror V θ θ θ θ M’ M s s’
Image formation by a Plane mirror • M is the object and M’ is the virtual image • Ray MV is incident normally to the plane mirror and it returns along its original path • s= object distance • s’= image distance • s=-s’
Image formation by a Plane mirror • Sign rules For the object distance: • When the object is on the same side of the reflecting or the refracting surface as the incoming light, s is positive For the image distance: • When the image is on the same side of the reflecting or the refracting surface as the outgoing light, s’ is positive
Image of an extended object V’ V Q’ Q θ θ y y’ θ θ M θ M’ s s’
Image of an extended object • Lateral magnification • Ratio of image height to object height • M=y’/y • Image is erect • m for a plane mirror is always +1 • Reversed means front-back dimension is reversed
Reflection on Concave and Convex mirrors Reflection at a Spherical Surface
Reflection at a Concave Mirror V C P P’
Graphical Methods for Mirrors Image formation on spherical mirrors
Graphical Method • Consists of finding the point of intersection of a few particular rays that diverge from a point of the object and are reflected by the mirror • Neglecting aberrations, all rays from this object point that strike the mirror will intersect at the same point
Graphical Method • For this construction, we always choose an object point that is not on the optic axis • Consists of four rays we can usually easily draw, called the principal rays
Reflection at a Concave Mirror V F C s at infinity s’= R/2
Reflection at a Concave Mirror • All reflected rays converge on the image point • Converging mirror • If R is infinite, the mirror becomes plane
Reflection at a Concave Mirror V F C s’ at infinity s= R/2
Reflection at a Concave Mirror 1/s+ 1/s’= 1/f Object image relation, spherical mirror
Reflection at a Convex Mirror F C s’ or s= R/2 s or s’ at infinity
Image formation on spherical mirrors • Sign rules For the object distance: • When the object is on the same side of the reflecting or the refracting surface as the incoming light, s is positive; otherwise, it is negative
Image formation on spherical mirrors • Sign rules For the image distance: • When the image is on the same side of the reflecting or the refracting surface as the outgoing light, s’ is positive; otherwise, it is negative
Image formation on spherical mirrors • Sign rules: For the radius of curvature of a spherical surface: • When the center of curvature C is on the same side as the outgoing light, the radius of curvature is positive, otherwise negative
Reflection at a Convex Mirror • The convex side of the spherical mirror faces the incident light • C is at the opposite side of the outgoing rays, so R is neg. • All reflected rays diverge from the same point • Diverging mirror
Refraction at spherical interface Refraction at a Spherical Surface
Refraction at a Spherical Surface na/s + nb/s’=0 At a plane refracting surface
Biconcave and biconvex thin lenses Graphical Method for Lenses
