. . Lens Formula and Magnification As we have a formula for spherical mirrors, we also have formula for spherical lenses. This formula gives the relationship between object- distance ( u ), image-distance ( v ) and the focal length ( f ).
The lens formula is expressed as ( . ) The lens formula given above is general and is valid in all situations for any spherical lens. Take proper care of the signs of different quantities, while putting numerical values for solving problems relating to lenses. Magnification The magnification produced by a lens, similar to that for spherical mirrors, is defined as the ratio of the height of the image and the height of the object.
Magnification is represented by the letter m . If h is the height of the object and h ′ is the height of the image given by a lens, then the magnification produced by the lens is given by, m = Height of the Image Height of the object = h ′ ( . ) Magnification produced by a lens is also related to the object-distance u, and the image-distance v . This relationship is given by Magnification (m ) = h ′ / h = v / u ( .
) Example . A concave lens has focal length of cm. At what distance should the object from the lens be placed so that it forms an image at cm from the lens? Also, find the magnification produced by the lens.
Solution A concave lens always forms a virtual, erect image on the same side of the object. Image-distance v = – cm; Focal length f = – cm; Object-distance u = ? Since or, – ( ) – – – – u = = − or, u = – cm Thus, the object-distance is cm. Magnification m = v/u m = − 10cm 30cm .
; The positive sign shows that the image is erect and virtual. The image is one-third of the size of the object. Example . A .
cm tall object