# A Particle is Moving at a Constant Speed V from a Large Distance Towards a Concave Mirror of Radius R Along Its Principal Axis. Find the Speed of the Image Formed by - Physics

Sum

A particle is moving at a constant speed V from a large distance towards a concave mirror of radius R along its principal axis. Find the speed of the image formed by the mirror as a function of the distance x of the particle from the mirror.

#### Solution

Given,
Radius of the concave mirror is R
Therefore focal length of the mirror,
$f = \frac{R}{2}$
Velocity of the particle, $V = \frac{dx}{dt}$
Object distance, u = −x

Using mirror equation,
1/v + 1/u = 1/f
On putting the respective values we get,
1/v + 1/-x= -2/R
⇒ 1/v = -2/R + 1/x = ( R- 2x )/ ( Rx )
∴ v = (Rx) /( R - 2x
Velocity of the image is given by V1
V^1= (dv)/dt = d/dt [(Rx)/ R-2x]

= [d/dx (Rx ) (R -2x)]- [d/dx ( R-2x )(Rx)]/ (R - 2x)^2

= R [ (dx/dt) (R - 2x )] - [ 2dx/dt x] /( R -2x )^2

=(R[(V) (R-2x)] - [ 2Vxx 0] )/( R-2x)^2

= VR^2/(2x -R )^2

Concept: Concave Mirror
Is there an error in this question or solution?
Chapter 18: Geometrical Optics - Exercise [Page 416]

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 18 Geometrical Optics
Exercise | Q 74 | Page 416

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