Physics 2102 Jonathan Dowling Lecture 37 MON 20 APR Optics Images Thin Lenses For small angles and thin lenses Convergent lens 1 1 1 p i f Convergent f positive Divergent f negative Divergent lens 1 1 1 n 1 f r1 r2 Lens maker s equation Images due to lenses An object placed beyond a convergent lenses focal point will produce a real inverted image on the other side of the lens This is the principle used in projectors An object placed between a convergent lens and its focal point will produce a virtual image on the same side as the object Divergent lenses always produce a virtual image on the same side as the object Real images have i positive in formulas virtual images have i negative Locating images by drawing rays A ray of direction initially parallel to the axis will pass through the focal point A ray that initially has a direction that passes through the focal point will emerge parallel to the central axis A ray going through the center of the lens will be undeflected The image of a point appears where all rays emanating from a point intersect Example An object 1 2cm high is placed 4cm from a bi convex lens with r1 10cm and r2 15cm Find the position and size of the image A second lens of focal length 6cm is placed 12cm to the right of the first lens Find the position and size of the new image Images from spherical mirrors Consider an object placed between the focal point and the mirror It will produce a virtual image behind the mirror When the object is at the focal point the image is produced at infinity If the object is beyond the focal point a real image forms at a distance i from the mirror 1 1 1 p i f i m p Check the signs lateral magnification Thin Lenses For small angles and thin lenses Convergent lens 1 1 1 p i f Convergent f positive Divergent f negative Divergent lens 1 1 1 n 1 f r1 r2 Lens maker s equation Locating images by drawing rays A ray of direction initially parallel to the axis will pass through the focal point A ray that initially has a direction that passes through the focal point will emerge parallel to the central axis A ray going through the center of the lens will be undeflected The image of a point appears where all rays emanating from a point intersect Images due to lenses An object placed beyond a convergent lenses focal point will produce a real inverted image on the other side of the lens This is the principle used in slide projectors An object placed between a convergent lens and its focal point will produce a virtual image on the same side as the object Divergent lenses always produce a virtual image on the same side as the object Real images have i positive in formulas virtual images have i negative Example An object 2cm high is placed 4cm from a bi convex lens with r1 10cm and r2 15cm and index of refraction n 1 5 Find the position and size of the image A second lens of focal length 6cm is placed 12cm to the right of the first lens Find the position and size of the new image
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