Image Formation and Mirrors

• Images can be found by looking inside a bag or in a bathroom mirror.
• Understanding the law of reflection of light is useful in understanding how images are formed.

Image Formation in Mirrors

• Images are formed in a mirror when light rays from an object are reflected.
• The object: the actual, physical source of light and incident rays.
• The image: the picture formed by the reflected rays.
• An object can be a light bulb, a candle, or anything that reflects light from another source.
• Images formed by reflection can be real or virtual.
• Real images: light rays intersect at the image, appearing inverted.
• Virtual images: light rays do not meet at the image, appearing erect (upright).
• Real images can be formed on a screen because light rays meet there.
• Virtual images cannot be seen on a screen.
• Object distance (d₀): the distance from the mirror to the object
• Image distance (dᵢ): the distance from the mirror to the image

Types of Mirrors

• Plane mirrors consist of a flat, two-dimensional surface.
• The Law of Plane Mirrors states the image is the same distance behind the mirror as the object is in front
• The image and object line up along the same normal.
• Images are upright but left-right reversed.
• Rays entering the eye diverge from the mirror's surface, creating a virtual image.
• The law of reflection applies to both light and sound waves.
• The angle of incidence equals the angle of reflection.

Spherical Mirrors

• Spherical mirrors are created from a spherical surface cut and polished to focus light from a point source to converge to a point image.
• Types are concave and convex mirrors.
• Concave mirrors: Reflect light from the inside of the sphere.
  • They converge light rays to a focus.
  • Images can be virtual or real, depending on the object's position.
  • The image is virtual, larger, and upright if the object is between the mirror and the focus.
  • The image is real and can be upside-down, larger, or smaller if the object is farther than the focus.
  • Common uses: shaving and makeup mirrors.
• Convex mirrors: Curve outward and reflects light from the outside of the cut sphere.
  • Reflected light appears to come from behind the mirror, creating a virtual image.
  • Objects appear smaller and farther apart.
  • Common uses: passenger-side wing mirrors in cars to widen field of view and minimize blind spots.

Features of Concave and Convex Mirrors

• Center of curvature (C): the center of the circle represented by the mirror’s arc.
• Focus (F): the point where parallel light rays converge; located on the inner part of the circle; equal to one-half the radius.
• Vertex (V): the point where the mirror crosses the principal axis.
• Principal axis: a line through the vertex, focus, and center of curvature.
• Focal length (f): the distance from the focus to the vertex of the mirror.
• Radius of curvature: the distance from the center of curvature to the vertex of the mirror, corresponding to the radius of the circle.

Ray Diagramming for Mirrors

• Ray diagrams trace the path of light to view a point on the image of an object.
• Lines with arrows (rays) are drawn for the incident and reflected rays.
  • Objects are represented by arrows with lengths indicating height.
  • Upward arrows mean the object is upright or erect
  • Downward arrows indicate the object is inverted.
  • Solid lines represent real objects
  • Dashed lines represent virtual objects.
• Ray diagramming is used to describe the location, size, orientation, and type of image formed by concave mirrors.

Ray Diagramming Rules

• Principal ray: leaves a point on the object parallel to the principal axis and passes through the focal point after reflection.
• Focal ray: leaves the same point on the object, passes through the focal point, and reflects parallel to the principal axis.
• Chief ray: leaves the same point on the object, passes through the center of curvature, and returns along the same path after reflection.

Applications of Mirrors

• Concave mirrors form different images depending on the object's distance from the center of curvature.
• Convex mirror images are always virtual, upright, and smaller than the object.
• Convex mirrors are used in:
  • Traffic safety mirrors to eliminate blind spots.
  • Lift trucks and large vehicles to prevent collisions.
  • Ceiling dome mirrors for surveillance in shops and offices
  • Cab front rearview mirrors to reduce blind spots for forklift trucks.
  • Portable inspection mirrors for security purposes.
  • Monitoring automated processes like quality control and packaging.

Lenses and Images

• Images are formed when light refracts at a boundary between two different materials.
• Lenses in the eyes form images that enable sight.

Types of Lenses

• A lens is a transparent material that refracts light to create an image.
• Converging lens (convex lens): thicker in the middle.
• Diverging lens (concave lens): thinner in the middle than at the edges.
• Principal axis: the line joining the centers of curvatures of the lens surfaces.
• Principal focus: the point where light rays converge.
• Focal length: the distance from the center of the lens to the principal focus.
• Light rays converge or diverge at another point due to refraction.
• Observers identify the point of convergence or divergence as the source of light.
• Diverging lenses always form virtual, upright, and smaller images, regardless of the object's position.
• Converging lenses form various images.