Lenses We will only consider “thin” lenses where the thickness of the lens is small compared to the object and image distances. Eugene Hecht, Optics, Addison-Wesley, Reading, MA,

Refraction at a Spherical Surface Uses the paraxial approximation Eugene Hecht, Optics, Addison-Wesley, Reading, MA, Ingle and Crouch, Spectrochemical Analysis

Biconvex Lens: Overlap of two spheres Position of l’: Position of l: Lensmaker’s Formula Ingle and Crouch, Spectrochemical Analysis

Convex Concave Basic Lenses

Eugene Hecht, Optics, Addison-Wesley, Reading, MA, Lens Makers’ Formula Determining the focal length of a lens: If d << R 1, R 2, make the thin lens approximation: f = focal length n = refractive index of lens material n m = refractive index of surrounding medium R 1 = radius of curvature of surface #1 R 2 = radius of curvature of surface #2 d = thickness of lens C R f

Simple Lenses Many different configurations: Sign Conventions for R values: C R f Sign of R V left of C + V right of C _ surface is flat ∞ www. wikipedia.org

Are you getting the concept? Calculate the focal length of a planoconvex lens of radius of curvature 60 mm and index of refraction of 1.5 in air using the thin lens approximation.

Parallel Rays Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Optical Center Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Tracing rays to determine the position of the image. Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Off Axis Rays Focus on the Focal Plane Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Chromatic Aberrations Eugene Hecht, Optics, Addison-Wesley, Reading, MA,  is dependent

Achromatic Doublet Ingle and Crouch, Spectrochemical Analysis

Spherical Aberrations Deviation from the paraxial approximation

Field Curvature Image and focal planes are actually spheres Eugene Hecht, Optics, Addison-Wesley, Reading, MA, 1998.

Comatic Aberration (Coma) Axial rays have different optical path lengths in an off-axis system.

Comatic Aberration (Coma) Eugene Hecht, Optics, Addison-Wesley, Reading, MA, Image has a comet-like tail

Astigmatism Rays in tangential and saggital planes have different focal points. f t = fcos  1 f s = f / cos  1 Ingle and Crouch, Spectrochemical Analysis

Lens Stops ApertureStopFieldStop Ingle and Crouch, Spectrochemical Analysis