Two objects ' A^' and ' B ' when placed in turns infront of...

Two objects ' $A^{\prime}$ and ' $B$ ' when placed in turns infront of a concave mirror, give images of equal size. The focal length of the concave mirror is $7.5 \mathrm{~cm}$ and size of object $A$ is three times the size of object $B$. The distance of $B$ from the mirror, if $A$ is placed $30 \mathrm{~cm}$ from the mirror, is : (a) $18 \mathrm{~cm}$ (b) $15 \mathrm{~cm}$ (c) $20 \mathrm{~cm}$ (d) $25 \mathrm{~cm}$

Two objects ' $A^{\prime}$ and ' $B$ ' when placed in turns infront of a concave mirror, give images of equal size. The focal length of the concave mirror is $7.5 \mathrm{~cm}$ and size of object $A$ is three times the size of object $B$. The distance of $B$ from the mirror, if $A$ is placed $30 \mathrm{~cm}$ from the mirror, is :
(a) $18 \mathrm{~cm}$
(b) $15 \mathrm{~cm}$
(c) $20 \mathrm{~cm}$
(d) $25 \mathrm{~cm}$

Key Concepts

Concave Mirrors

Concave mirrors are curved mirrors that converge parallel light rays to a focal point. Their behavior in image formation is governed by specific geometric relationships, which determine whether an image is real or virtual, inverted or erect, and magnified or reduced. This concept is fundamental in understanding how object placement affects the properties of the image produced.

Focal Length

The focal length of a mirror is the distance from the mirror's surface to its focal point, where light rays parallel to the mirror’s principal axis converge after reflection. It is a crucial parameter in mirror formulas and determines the scale and nature of the image. In problems involving concave mirrors, a known focal length is essential for calculating object and image distances.

Mirror Equation

The mirror equation relates the object distance, image distance, and focal length through the formula 1/f = 1/u + 1/v. This equation is pivotal for solving problems involving concave mirrors, allowing one to determine unknown distances when the other two are known. Understanding this relationship is key to analyzing how the position of an object affects the characteristics of the image.

Magnification

Magnification in mirror systems is defined as the ratio of the image height to the object height, and is also given by the negative ratio of the image distance to the object distance (m = -v/u). This concept links the physical size of the object and image to their respective distances from the mirror, and is essential for problems where image size comparisons or scaling are involved.

Please give Ace some feedback