The Mirror Equation

Laws of Reflection:

• Law of Reflection: The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
• Angle of incidence and the angle of reflection are equal.

Mirror Equation:

• The derivation of the mirror equation can be done using similar triangles.
• Sign conventions:
• The object distance is positive when the object is placed in front of the mirror.
• The image distance is positive when the image is formed in front of the mirror.
• The focal length is positive for a concave mirror and negative for a convex mirror.
• Mirror Equation: $$ \frac {1}{v}+\frac {1}{u}=\frac {1}{f} $$

Focal length and Radius of curvature:

• Focal point is the point where parallel rays of light converge after reflection from a mirror.
• Radius of curvature is the distance between the pole of the mirror and the center of curvature.
• Relationship between focal length and radius of curvature: $$ R = 2f $$

Magnification:

• Definition of magnification: The ratio of the height of the image to the height of the object.
• Magnification formula for plane and spherical mirrors: $$ m=\frac{h’}{h} = \frac{-v}{u} $$
• Explanation:
• The negative sign indicates that the image is inverted for a concave mirror.
• The positive sign indicates that the image is upright for a convex mirror.

Ray Diagrams for Mirror:

• Construction and analysis of ray diagrams for various object positions allows students to visualize the formation of images.
• Determination of image location, size, and orientation can be done using ray diagrams.

Special Cases of Mirror Equation:

• Object at infinity: The image is formed at the focal point.
• Object at focus: The image is formed at infinity.
• Object at the centre of curvature: The image is formed at the centre of curvature.
• Virtual and real images: A virtual image cannot be projected onto a screen, while a real image can.

Applications of Mirror Equation:

• Image formation in telescopes, microscopes, and other optical instruments: The mirror equation can be used to design and analyze optical systems.
• Ray tracing in optical systems: The mirror equation can be used to trace the path of light rays through an optical system.
• Solving numerical problems based on mirror equation: Practice solving numerical problems to improve your understanding of the concept.

Aberration in Mirrors:

• Spherical aberration occurs when light rays from different parts of the object are focused at different points.
• Coma occurs when spherical wavefronts are reflected from a parabolic mirror.

Image Defects and Correction:

• Spherical aberration-corrective measures:
  • Use of aspherical mirrors
• Use of a combination of mirrors
• Coma-corrective measures:
  • Use of parabolic mirrors
• Use of a combination of mirrors

References:

• NCERT Physics Class 11, (Chapters 1, 11)
• NCERT Physics Class 12, (Chapters 9)