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Unformatted text preview: Section 2: Spherical lenses Section 2: Spherical lenses We will introduce spherical lenses and the paraxial approximation. This will be applied to determine object and image distances. Learning outcomes: • Explain why spherical lenses are important • State the paraxial approximation and be able to describe its implications • D e f i n e focal length and magnification for an optical stem ©AGK 2010 Geometric optics 1: Lenses and lens combinations 28 syste Sample problems Sample problems Try these problems from Hecht: • 5.6 Prove that the minimum separation between njugate al bject and image points for a thin positive conjugate real object and image points for a thin positive lens is 4 f • 5.9 An object 2 cm high is positioned 5 cm to the right of a positive thin lens with a focal length of 10 cm. Describe e resulting image completely using both the Gaussian the resulting image completely, using both the Gaussian and the Newtonian equations. ©AGK 2010 Geometric optics 1: Lenses and lens combinations 29 • Solutions are in the back of the textbook Spherical lenses Spherical lenses • Spherical lenses can be made easily by grinding • Known for a long time (references date back to the Greeks) herical lenses are not stigmatic • Spherical lenses are not stigmatic • R e s u l t in aberrations Detail from ‘Cardinal Nicholas of ©AGK 2010 Geometric optics 1: Lenses and lens combinations 30 Rouen’ by Tommaso Da Modena (c. 1325 ‐ 1379) Lens grinding Lens grinding • Two approximately spherical surfaces will become more spherical with abrasion • T h e r e f o r e spherical lenses are relatively easy to make (see gure in Hecht) figure in Hecht) Grinding tool Lens blank Grinding paste (diamond) ©AGK 2010 Geometric optics 1: Lenses and lens combinations 31 Lens grinding Lens grinding Polishing shop at Eastman Kodak ©AGK 2010 Geometric optics 1: Lenses and lens combinations 32 Craftsman with multiple lens block Modern grinding machine Spherical lenses Spherical lenses • Spherical lenses have two spherical surfaces • W e need to be able to calculate the object plane focal length and the image plane focal length elated to radius of curvature d refractive index • Related to radius of curvature R and refractive index n 1 • S t a r t with calculations for a single surface n n 1 ©AGK 2010 Geometric optics 1: Lenses and lens combinations 33 Spherical lenses Spherical lenses • Spherical lenses have two spherical surfaces • W e need to be able to calculate the object plane focal...
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 Winter '10
 Kirk
 GEOMETRIC OPTICS

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