Define a concave mirror. Draw a ray diagram to show the formation of a real, inverted, and magnified image by a concave mirror. State the position of the object and the image. Also, write the mirror formula and explain each term involved in it.

Q: Define a concave mirror. Draw a ray diagram to show the formation of a real, inverted, and magnified image by a concave mirror. State the position of the object and the image. Also, write the mirror formula and explain each term involved in it.

Definition of a Concave Mirror \nA spherical mirror whose reflecting surface is curved inwards (facing towards the center of the sphere) is called a concave mirror. Concave mirrors are converging mirrors because they converge parallel rays of light falling on them to a single point called the principal focus. Image Formation by a Concave Mirror \nWhen an object is placed between the principal focus ($F$) and the center of curvature ($C$) of a concave mirror, the characteristics of the image formed are as follows: Position of Object: Between focus ($F$) and center of curvature ($C$). Position of Image: Beyond the center of curvature ($C$). Nature of Image: Real and inverted. Size of Image: Magnified (larger than the object). Ray Diagram Description \nTo construct the ray diagram: Draw a principal axis with a concave mirror, marking the pole ($P$), focus ($F$), and center of curvature ($C$). Place an object $AB$ between $F$ and $C$. Take a ray parallel to the principal axis from point $B$; after reflection, it passes through the principal focus $F$. Take a second ray passing through the principal focus $F$; after reflection, it travels parallel to the principal axis. The two reflected rays intersect beyond $C$ at point $B'$, forming a real and inverted image $A'B'$. Mirror Formula \nThe mirror formula relates the object distance ($u$), image distance ($v$), and focal length ($f$) of a spherical mirror. The mathematical expression is: $$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$| Explanation of Terms: $f$ (Focal length): The distance between the pole ($P$) and the principal focus ($F$) of the mirror. $v$ (Image distance): The distance of the image from the pole ($P$) of the mirror. $u$ (Object distance): The distance of the object from the pole ($P$) of the mirror. \nThis formula is valid under all conditions for all spherical mirrors, provided New Cartesian Sign Conventions are strictly followed.

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Definition of a Concave Mirror 
A spherical mirror whose reflecting surface is curved inwards (facing towards the center of the sphere) is called a concave mirror. Concave mirrors are converging mirrors because they converge parallel rays of light falling on them to a single point called the principal focus. Image Formation by a Concave Mirror 
When an object is placed between the principal focus ($F$) and the center of curvature ($C$) of a concave mirror, the characteristics of the image formed are as follows: Position of Object: Between focus ($F$) and center of curvature ($C$). Position of Image: Beyond the center of curvature ($C$). Nature of Image: Real and inverted. Size of Image: Magnified (larger than the object). Ray Diagram Description 
To construct the ray diagram: Draw a principal axis with a concave mirror, marking the pole ($P$), focus ($F$), and center of curvature ($C$). Place an object $AB$ between $F$ and $C$. Take a ray parallel to the principal axis from point $B$; after reflection, it passes through the principal focus $F$. Take a second ray passing through the principal focus $F$; after reflection, it travels parallel to the principal axis. The two reflected rays intersect beyond $C$ at point $B'$, forming a real and inverted image $A'B'$. Mirror Formula 
The mirror formula relates the object distance ($u$), image distance ($v$), and focal length ($f$) of a spherical mirror. The mathematical expression is: $$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$| Explanation of Terms: $f$ (Focal length): The distance between the pole ($P$) and the principal focus ($F$) of the mirror. $v$ (Image distance): The distance of the image from the pole ($P$) of the mirror. $u$ (Object distance): The distance of the object from the pole ($P$) of the mirror. 
This formula is valid under all conditions for all spherical mirrors, provided New Cartesian Sign Conventions are strictly followed.