The speed at which the image of the luminous point object is...

The speed at which the image of the luminous point object is moving, if the luminous point object is moving at speed $v_{0}$ towards a spherical mirror, along its axis, is : (Given : $R=$ radius of curvature, $u=$ object distance $)$ (a) $v_{t}=-v_{o}$ (b) $v_{t}=-v_{o}\left(\frac{R}{2 u-R}\right)$ (c) $v_{i}=-v_{0}\left(\frac{2 u-R}{R}\right)$ (d) $v_{i}=-v_{o}\left(\frac{R}{2 u-R}\right)^{2}$

The speed at which the image of the luminous point object is moving, if the luminous point object is moving at speed $v_{0}$ towards a spherical mirror, along its axis, is :
(Given : $R=$ radius of curvature, $u=$ object distance $)$
(a) $v_{t}=-v_{o}$
(b) $v_{t}=-v_{o}\left(\frac{R}{2 u-R}\right)$
(c) $v_{i}=-v_{0}\left(\frac{2 u-R}{R}\right)$
(d) $v_{i}=-v_{o}\left(\frac{R}{2 u-R}\right)^{2}$

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Key Concepts

Differentiation in Optics

Differentiation in optics is used to study how the positions of images change as objects move. By differentiating the mirror equation with respect to time, one can relate the rate of change of the image distance to the rate of change of the object distance, thereby analyzing the dynamics of image formation.

Optical Sign Conventions

Optical sign conventions provide a systematic way to assign positive and negative directions to distances, focal lengths, and other parameters in mirror and lens equations. These conventions are vital for ensuring consistency and correctness in calculations involving image formation and movement in optical systems.

Mirror Equation

The mirror equation is a cornerstone of geometric optics that relates the object distance, image distance, and the focal length of a mirror using the formula 1/u + 1/v = 1/f. This relation is key to determining where an image will be formed relative to a mirror based on the object's distance from the mirror.

Focal Length and Radius of Curvature

For spherical mirrors, the focal length is directly related to the radius of curvature by the relationship f = R/2. This connection is important because it ties the physical dimensions of the mirror to its optical properties, influencing how the mirror forms images.

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