Mirrors and Lenses

Optics Terminology and Assumptions Focus or focal point – point from which a portion of waves diverge or on which they converge Optical Axis – central axis through optical elements Principle of Reversibility – if source and image are interchanged, the route the light follows is unchanged An object (in object space) is related to an image (in image space) as conjugate points (i.e. the object would be equally well imaged at either point) Real image – a luminous image of the object would appear if a screen was placed at the focus in image space Virtual image – no luminous image of the object would appear if a screen was placed at the focus Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Planar Mirrors Front surface mirrors Usually “glass” coated with Al Eugene Hecht, Optics, Addison-Wesley, Reading, MA, object image

Spherical Mirror Formula Use external angle theorem: exterior angle of a triangle is equal to the sum of the opposite interior angles Make paraxial approximation: Assume  1 is small so that sin  1 ~  1 (in radians) cos  1 ~ 1 tan  1 ~  1 Ingle and Crouch, Spectrochemical Analysis

Eugene Hecht, Optics, Addison-Wesley, Reading, MA, Spherical Mirrors ConvexConcave Virtual Image Real Image

Focal Length of Spherical Mirrors Ingle and Crouch, Spectrochemical Analysis + for concave (R<0) - for convex (R>0) General Mirror Formula:

Producing Collimating Light with Spherical Mirrors Ingle and Crouch, Spectrochemical Analysis

Focal Plane Image formed off axis in the focal plane. Useful for separating light traveling at different angles. Ingle and Crouch, Spectrochemical Analysis

Predicting Where Images Will Form Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Image Reflected From a Spherical Mirror Eugene Hecht, Optics, Addison-Wesley, Reading, MA, Transverse Magnification: M t = -s i /s o + M t signals an erect image - M t signals an inverted image |M t | >1 signals a magnification |M t | <1 signals a minification with the following sign conventions: s o /s i + for real object/images o /s i + for real object/image s o /s i - for virtual object/images o /s i - for virtual object/image

Are you getting the concept? Describe the geometric conditions that must exist to see a magnified upright image in a spherical mirror.