for u , v and f in equation ( . ). . .
Lateral magnification in spherical mirrors The lateral (or) transverse magnification m is defined as the ratio of the height of the image to the height of the object .The height of the object and image are measured perpendicular to the principal axis. magnification heightof theimage heightof theobject ( ) ( ) ( ) h h ′ h h ′ ( . ) Applying proper sign conventions for equation ( . ), ′ ′ = ′ A B AB PA PA ′ ′ =−′ ′ =− =− A B h PA v PA u ,AB h, , −′ = − h h u On simplifying we get, h h u ′ =− ( .
) Using mirror equation, we can further write the magnification as, h h u ′ = − ( . ) The students are advised to refresh themselves with the image tracing for the concave and convex mirrors for various predetermined positions of the object; the position of image, nature of image etc., from th Standard, Science Book . Note ′ ′ = ′ A B PD A F PF As, PD = AB the above equation becomes, ′ ′ = ′ A B AB A F PF ( . ) From equations ( .
) and ( . ) we can write, PA PA A F PF ′ = ′ As, ′ ′ A F=PA - PF , the above equation becomes, PA PA PA PF PF ′ = ′− ( . ) PA, PA ' and PF are mere distances; here we use sign conventions so that the expression that is derived will be a general one. The general expression thus obtained will be valid for the situations other than the one shown in figure.
∴ substituting PA = – u , PA' = – v and PF = – f in equation ( . ), PA u PA PF =− ′ =− =− , , All the three distances are negative as per sign convention, because they are measured to the left of the pole. Now, the equation ( . ) becomes, − = −−− u On further simplification, u