Image Formation by Mirrors §

Introduction §

Mirrors are reflective surfaces that obey the laws of optics, particularly the law of reflection, to form images. They are a fundamental topic in optics, a branch of physics. There are two main types of mirrors used for image formation: plane mirrors and curved mirrors, which include concave and convex mirrors.

Plane Mirrors §

• Law of Reflection: The angle of incidence is equal to the angle of reflection.
• Image Characteristics: The image formed by a plane mirror is virtual, upright, and of the same size as the object. It appears to be the same distance behind the mirror as the object is in front.

Curved Mirrors §

Concave Mirrors §

• Shape: Concave mirrors curve inward, resembling a portion of the interior of a sphere.
• Focal Point: Parallel rays of light reflect and converge at a point called the focal point.
• Image Formation: Depending on the object’s distance from the mirror, the image can be real or virtual, upright or inverted, and magnified or diminished.

Convex Mirrors §

• Shape: Convex mirrors curve outward.
• Focal Point: Parallel rays of light appear to diverge from a focal point behind the mirror.
• Image Characteristics: The image is always virtual, upright, and smaller than the object.

Mathematical Representation §

• Mirror Equation: $\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$
  • Where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance.
• Magnification: $m=-\frac{d_i}{d_o}$
  • A negative magnification indicates an inverted image.

Historical Context §

Mirrors have been used since ancient times, initially as polished surfaces of natural materials. The understanding of optical principles related to mirrors has evolved significantly, contributing to various fields like astronomy, architecture, and even psychology.

Examples §

• Telescopes: Concave mirrors are used in telescopes to gather and focus light from distant objects.
• Vehicle Mirrors: Convex mirrors are used as rear-view mirrors in vehicles to provide a wider field of view.

Test Questions §

1. STARTI [Basic] Question: What type of image is formed by a plane mirror? Back: The image formed by a plane mirror is virtual, upright, and of the same size as the object. ENDI
2. STARTI [Basic] Question: How does the focal point of a concave mirror differ from that of a convex mirror? Back: The focal point of a concave mirror is a real point where light rays converge, while for a convex mirror, it is a virtual point from which light rays appear to diverge. ENDI
3. STARTI [Basic] Question: If an object is placed at twice the focal length of a concave mirror, describe the image. Back: The image will be real, inverted, and of the same size as the object, formed at a distance equal to twice the focal length on the same side as the object. ENDI

For further reading on specific aspects of image formation by mirrors, refer to the following notes:

• Laws of Reflection and Refraction
• Optical Instruments and Their Uses
• Historical Development of Optics