Question #dafd5
1 Answer
Let at an instant the image distance be
We know that the cojugate foci relation of spherical mirror is as follows.
#color(blue)(1/v+1/u=1/F......[1])#
Imposing sign convention for convex mirror
#color(green)(1/v-1/u=1/F.....[2])#
#color(green)(=>1/v=1/u+1/F)#
#color(green)(=>1/v=(u+F)/(uF))#
#color(green)(=>v/u=(F)/(u+F))#
#color(green)(=>v/u=(F)/(u+F)<1.....[3])#
Now differentiating equation [2] w.r to
#color(violet)(-1/v^2(dv)/(dt)+1/u^2(du)/(dt)=0.....[4])#
#color(violet)(=>1/v^2(dv)/(dt)=1/u^2(du)/(dt))#
Now
And
So equation [4] becomes
#color(red)(1/v^2xxv_i=1/u^2xxv_o)#
#color(red)(=>v_i/v_o=v^2/u^2.....[5])#
Utilising equation [3] and [5] we can say
#color(red)(v_i/v_o=F^2/(u+F)^2)#
So
And
Since
So we can support option (1) and (3) to be correct