A point object P is moving towards left with speed 5 mm/sec parallel to optical axis of a concave mirror of focal length f = 20 cm. The seperation between object and optical axis is 1 cm. Find velocity of image of object in vector form when foot of perpendicular from object on the optical axis is at a distance 30 cm from pole.

Options

A. `vecV_(i)=20hati+4hatjmm//sec`
B. `vecV_(i)=20hati+hatjmm//sec`
C. `vecV_(i)=20hati-hatj//sec`
D. `vecV_(i)=20hatimm//sec`

Explanation

`(1)/(v)+(1)/(-30)=(1)/(-20)`
`v=-60`
`m=(y_(i))/(y_(o))=(v)/(u)`
`y_(i)=-2cm`
for `vec_(v)_(1),vecv_(1)" "vecv_(1)=-(v^(2))/(u^(2))(vecv_(p))` ltbr. `=-4(-5)=20mm//sec`
for `vecv_(2)" "vecv_(2)" "implies(y_(i))/(y_(o))=(v)/(u)`
`y_(i)u=-y_(o)v`
`(dy_(i))/(dt)(u)+y_(i)(dy)/(dt)=-y_(0)(dv)/(dt)`
`(dy_(i))/(dt)(-30)+(-2)(-5)=-(20)`
`(dy_(i))/(dt)=1mm//sec`
`V_(i)=20hati+hatjmm//sec`