Understanding Reflection and Mirrors

• Reflection occurs when light bounces off a surface and returns to the same medium it was traveling in.

Types of Reflection

• Regular or Specular Reflection happens on smooth surfaces.
• Diffuse Reflection happens on rough surfaces.

Laws of Reflection

• The angle of incidence (θi) equals the angle of reflection (θr).
• The incident ray, the normal, and the reflected ray all lie on the same plane.

Mirrors

• A mirror is any smooth surface that produces a regular reflection of light.
• The two main types of mirrors are plane mirrors and spherical mirrors.

Plane vs Spherical Mirrors

• A plane mirror is a flat, smooth, mirrored surface.
• Plane mirrors make the image clear and undistorted.
• Examples of plane mirrors: bathroom mirrors, dressing room mirrors, periscopes, and handheld cosmetic mirrors.
• A spherical mirror has a consistent curve and constant radius of curvature.
• A spherical mirror is a mirror that's a sphere-shaped mirror.
• Examples of spherical mirrors: shaving mirrors, reflectors in flashlights and headlights, solar concentrators, telescopes, passenger-side mirrors in cars, security mirrors, and dental mirrors.

L.O.S.T. Method

• Images formed by mirrors have qualitative properties
• This method helps in remembering and describing the properties of images: Location, Orientation, Size, and Type.
• Location of the image depends on the location of the object.
• Orientation refers to how an image is oriented relative to the original object
• Upright Image: An upright image is oriented in the same direction as the object.
• Inverted Image: An inverted image is oriented in the opposite direction as the object.
• Size of the image depends on the size and location of the object; it can be larger (>1), same size (=1), or smaller (<1).
  • Magnification is the ratio of the image dimensions to the object dimensions

Type of Image

• Real Image: formed by the actual intersection of reflected rays and can be projected on a screen.
• Virtual Image: formed behind the mirror and is always upright relative to the object, cannot be projected on a screen.

Qualitative characteristics of Image

• Location of image, same distance as the object (behind mirror).
• Orientation of image is upright, but laterally inverted.
• The size of the image is the same size as the object.
• The type of image is a virtual image.
• Lateral inversion is when the left side of an object appears on the right side of the image in a plane mirror.
• Spherical mirrors are mirrors cut out from a spherical reflecting surface

Types of Spherical Mirror

• Concave mirrors (converging mirrors) cause parallel incident rays to converge at a focal point.
• Convex mirrors (diverging mirrors) cause parallel incident rays to diverge after reflection.
• Center of Curvature (C): the center of the sphere from which the mirror was taken.
• Vertex (V): the center of the mirror.
• Focal point (F): the point where the reflected rays meet in concave mirrors, or appear to come from behind the mirror in convex mirrors.

Images Formed by Spherical Mirrors (Concave)

• Concave mirrors can produce real or virtual images depending on the distance between the mirror and the object.

Two Rules of Reflection for Concave Mirrors:

• Any incident ray traveling parallel to the principal axis will pass through the focal point upon reflection.
• Any incident ray passing through the focal point will travel parallel to the principal axis upon reflection.
• Location of the image in a concave mirror impacts characteristics such as: Between the object and F, Beyond C, At C etc.
• Concave mirrors create images between C and F, or behind the mirror, etc.
• Summary of Qualitative Characteristics of Images Formed in Concave Mirrors: location of the image, orientation, size etc.

Two Rules of Reflection for Convex Mirrors:

• Any incident ray traveling parallel to the principal axis will reflect so that its extension passes through the focal point.
• Any incident ray traveling towards the mirror so that its extension passes through the focal point will reflect parallel to the principal axis.
• Convex Mirrors always renders virtual images; smaller/upright.
• A concave mirror produces real or virtual images, which sizes depend on distance.
• A convex mirror always produces virtual, upright, and smaller images.
• Image formed by a convex mirror is never real because reflected rays spread out

Mirror Equation and Magnification

• The mirror equation relates the object distance (do), image distance (di), and focal length (f): 1/f = 1/do + 1/di
• M = hi/ho = -di/do.
• f is positive for concave mirrors and negative for convex mirrors.
• di is positive for real images and negative for virtual images.

Refraction

• Refraction is the change in the direction of light when it passes from one medium to another with different optical density.
• The incident ray, the refracted ray, and the normal all lie on the same plane.
• Light refracted away from the normal goes from more to less dense.
• When light passes obliquely from a less dense to a denser medium, it is refracted toward the normal

Snell's Law

• Snell's Law relates the indices of refraction of two media and the angles from the normal: n₁ sin θ₁ = n₂ sin θ₂.

Lenses

• Lenses are pieces of transparent glass that concentrates or disperses light rays through refraction.
• Spherical lenses are pieces of glass or transparent material with at least one spherical surface, either convex or concave.
• Convex lenses (converging lenses) are thicker at the middle than at the edges.
• Concave lenses (diverging lenses) are thicker at the edges than at the middle.
• In lenses, real images are on the opposite side of the lens from the object, while virtual images are on the same side.
• Optical Center: the point through which all light passes without being bent.
• The focal length is the distance from the optical center of the lens to the principal focus.
• The principal axis is the line joining the optical center and the principal focus.
• There are two focal points, one in front and one at the back.

Three Rules of Refraction for Convex Lenses:

• Any incident ray traveling parallel to the principal axis will refract through the lens and travel through the focal point on the opposite side.
• Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
• Any incident ray that passes through the center of the lens will continue in the same direction.
• Images can be formed by a Convex lens at the: Beyond 2F, At 2F, Between 2F and F etc.
• Object location has implications the resulting image such as inverted type, real image etc etc

Summary of the Qualitative Characteristics of an Image Formed in a Convex Lens in Various Locations

• Includes :location of the image, orientation of the image, the type of mirror used etc
• L.O.S.T. Methods, the object location, and effects of light.
• The three rules of refraction for concave lenses: (1) parallel rays refract and travel in line with the focal point, (2) rays towards focal point refract and travel parallel, (3) rays through the center continue in the same direction.
• Convex Lenses, concave lens: at F, at 2F etc.
• The image formed by a convex lens can be either real/inverted or virtual/upright.

Lens Equation and Magnification

• The lens equation is 1/f = 1/do + 1/di, relating object distance (do), image distance (di), and focal length (f).
• The magnification equation is M = hi/ho = -di/do.
• For the Lens Equation & Magnification Formula & Variables:
  • • d0 (distance of object to lenses) +
  • • di + real image, di - virtual image
  • • ho + upright image, ho _ inverted image