Now let us use these rules to show the formation of images when the object is placed at different places infront of the convex mirror (see fig. - 20)

AB is the object placed at any point on the principal axis infront of the convex mirror. Using Rule (1) and Rule (3), we get an erected, diminished, and virtual image between P and F on the back side of the mirror. This image can not be caught on screen and visible only in the mirror. Hence this is a virtual image. Verify this with an experiment.

Using these rules, draw ray diagrams to show formation of images when an object is placed at different positions and note down your conclusions. Verify your results experimentally.

You may get the image at a particular distance when you place the object at a certain distance. Do you find any relation between the object distance(u) and the image distance(v)?

Derivaton of formula for curved mirrors Observe figure 21. The ray from the top (B) of the object AB is emanating parallel to principle axis and striking the mirror at X. This ray passes through F after reflection. Another ray starting from B, passes through centre of curvature (C) and strikes the mirror at Y. This ray returns back in the same direction after reflection. There two rays XBI and YBI are meeting at BI . So BI is the image of B. Hence the image of AB is AI BI . From the above figure - 21. ΔABC, ΔAI BI C are similar triangles AB/AI BI = AC/ACI ..... (1) Draw a line XPI perpendicular to the principle axis. Similar ΔPIXF and ΔAI BI F are similar triangles PIX/AI BI = PIF/AIF ..... (2)