Question

Which of the following is correct for convex mirror? (a) m =I/O (b) m =V/u (c) m = I² /O² (d) m= V² /u² please if you know then only please tell with your explanation ​

Answer 1

Explanation:

We know mirror formula,

1/v + 1/u = 1/f

if I assumed mirror doesn't change , then focal length will be constant.

now, differentiate with respect to time ,

-1/v² dv/dt - 1/u² du/dt = 0

⇒u² dv/dt = -v² du/dt

⇒dv/dt = -(v/u)² du/dt

magnification , m = v/u

∴ dv/dt = -m² du/dt

⇒Vim = -m² Vom

Here, Vim = velocity of image with respect to mirror

Vom = velocity of object with respect to mirror.

Now, come to the point,

given, mirror is convex mirror,

And we have to find out ratio of speed of object to the speed of its real image .

But we know, practically real image can't formed we with help of convex mirror.

theorically, ratio of speed of object to the speed of image = -1/m² , where m is magnification .