Question

a plane mirror is approaching you at a speed of 10cm/s.you can see your image in it.at what speed will your image approach you

Answer 1

If a plane mirror is approaching to you with the speed of 10cm/s then at 1st second the distance b/w object and mirror will be 10, so the distance b/w object and image will be 2*10=20 b'coz in plane distance b/w object to mirror is same to the distance from image to mirror. So the image will be approaching with the speed of 20cm/s.

Hope this help you.

Answer 2

we know,
formula,
1/v + 1/u = 1/f

differentiate all with respect to time
-dv/dt×1/v² - du/dt ×1/u² = 0

for only one mirror f = constant
so df/dt =0

now,
dv/dt× 1/v² = -du/dt× 1/u²

dv/dt = -(v/u)² du/dt

here dv/dt = velocity of image with respect to mirror
so, dv/dt = Vim (let )

and du/dt = velocity of object with respect to mirror .
du/dt = Uom (let )

then ,
Vim = -(v/u)² Uom

for plane mirror ,
v = u
So,
Vim = -Uom

now, questions ,
Uo = 10 cm/sec
so,

Vi - Vm = -( 10 - Vm)

because is at rest so,
Vm =0

so, Vi = -10 cm/sec

hence , image moves opposite direction of object . with speed 10cm/sec
but question ask ,
velocity of image with respect to observer

so, Vio =Vi - Vo
= -10 -10 = -20cm/sec

hence, image approach to observer with speed 20cm/sec