# 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**