Cartesian Sign Convention for spherical mirrors Example . A convex mirror used for rear-view on an automobile has a radius of curvature of . m. If a bus is located at .
m from this mirror, find the position, nature and size of the image. Solution Radius of curvature, R = + . m; Object-distance, u = – . m; Image-distance, v = ?
Height of the image, h ′ = ? Focal length, f = R / = + . m = + . m (as the principal focus of a convex mirror is behind the mirror) Since or, = + .
= + . m The image is . m at the back of the mirror. Magnification, m = ' = − = – .
m . m = + . The image is virtual, erect and smaller in size by a factor of . .
Example . An object, . cm in size, is placed at . cm in front of a concave mirror of focal length .
cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and the size of the image. Solution Object-size, h = + .
cm; Object-distance, u = – . cm; Focal length, f = – . cm; Image-distance, v = ? Image-size, h ′ = ?
cm The screen should be placed at . cm in front of the mirror. The image is real. Also, magnification, m = ' = − or, h ′ = – v h u = ( .5cm) ( .0cm) ( .
cm) Height of the image, h ′ = – . cm The image is inverted and enlarged.