Saved Bookmarks
| 1. |
Derive the relation f=R/2 in the case of a concave mirror. |
|
Answer» <P> Solution :When a parallel beam of LIGHTIS incident on a CONCAVE mirror, the rays are paraxial ,i.e. they are incident at a point M , and make a small angle with principal axis. The reflected ray converges at a F on the principal axis. The point F is called the focus of the mirror ,the distance between the principalfocus and the pole is called focal LENGTH (f).Consider a ray parallel to the principal axis stricking the mirror at M, then `angleMFD=angleCMF+angleMCF=theta+theta=2theta` `angleMFD` is the external angle of the `angleMCF` In `triangle^"le"` MCD , `tan theta ="MD"/"CD"`...(1) In `triangle^"le"` MFD , tan `2theta ="MD"/"FD"` ...(2) `theta` is small , So `tan theta~~ theta , tan 2 theta ~~ 2 theta` , Substituting tan `theta` and tan `2theta` in the equations, `theta="MD"/"CD", 2theta="MD"/"FD"` `2xxcancel(MD)/(CD)=CANCEL(MD)/(FD) rArr 2/(CD)=1/(FD)` on CD =2FD Point D is very close to point P. `therefore DF ~~ PF ~~ f` and DC=PC=R `2/(CP)=1/(FP)`CP=3FP R=2f `f=R/2` 
|
|