Prozorov_27 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURES 27 Reflection and refraction at a spherical surface. Lenses. refraction PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 2 images formed by refraction PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 3 objects, images, and light rays o Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if the pass from a material of one index to another. PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 4 constructing the image from a plane mirror PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 5 constructing the image from a plane mirror PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 6 constructing the image from plane mirror PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 7 magnification Object’s height Image’s height y’ y Both y and y ’ can be negative if item is upside down! Magnification y m y If m > 0, image is upright. If m < 0, image is inverted. Example: For a plane mirror, m = +1 PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 8 reverse image B’ A’ C’ A B C Front and back are reversed Image on a plane mirror is virtual, upright and reversed. PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 9 image of an image Example: Two plane mirrors at 45° 1 2 PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 10 Image of an image Image for mirror 1 / Object for mirror 2 1 Object for mirror 1 Image for mirror 2 Use first image as an object for second mirror. Easier… 2 PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 11 spherical mirrors object Optic axis R C object Optic axis V C = center of curvature V = vertex R = radius of curvature R V Concave R > 0 C PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University Convex R < 0 26 October 2011 12 reflections from a spherical mirror PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 13 concave spherical mirror a + 2q + p - b = p f +q +p - b = p 2 If α is small (paraxial approximation), h s h tan s h tan R tan Thus, 1 s a h b C h h 2h s s R 1 2 s R f qq Independent of h s R s’ valid for all rays (with small α) PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 14 focal distance, focal point If object is very far, incoming rays are all parallel and s ∞ Rays converge at one point called the focal point F 1 1 2 f R f R 2 Focal length (spherical mirror) C F f (focal length) 1 1 1 s s f PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 15 the focal point and focal length o The focal point is at half of the mirror’s radius of curvature. o All incoming rays will converge at the focal point. PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 16 getting the image 1 ray parallel to the axis, reflection goes through F 1 ray to vertex, reflection at equal angle If a screen or a photographic plate is placed here, image will form on it Image is real and inverted. PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University F s>0 s’ > 0 26 October 2011 17 magnification (spherical mirror) y y tan s s y q q m y’ s’ s y s y s s m s It looks a little odd: image seems to be in front of mirror (and we’re used to plane mirrors, where it’s behind) PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 18 the convex spherical mirror • If you imagine standing inside a shiny metal ball to visualize the concave spherical mirror, imagine standing on the outside to visualize the concave spherical mirror. PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 19 convex spherical mirror Everything is the almost the same for the convex mirror, except R < 0, so f = R/2 < 0. Image is virtual, smaller and upright. F PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 20 the convex spherical mirror o The convex spherical mirror cannot produce a real image regardless of the position of the object. PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 21 The Hubble Space Telescope o The HST has a spherical mirror. Unfortunately, it was ground to the wrong dimensions by 1/50 the width of a human hair over a mirror as large as a person. o Replacing the mirror was unthinkable. The final solution was an electronic adjustment to the photodiode array which converts the optical image to digital data. PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 22 summary: graphical method for mirrors PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 23 PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 24 refraction within a sphere PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 25 thin lenses PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 26 thin lenses PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 27 graphical methods for lenses PHYS222 - Lecture 27 - Prof. Ruslan Prozorov - Iowa State University 26 October 2011 28 ...
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