Unit 1: Waves Lesson: Mirrors and Reflection of Light
The objects that we see can be placed into one of two categories: luminous objects and illuminated objects. Luminous objects are objects that generate their own light. Illuminated objects are objects that are capable of reflecting light to our eyes. The sun is an example of a luminous object, while the moon is an illuminated object.
Line of Sight
You can only view the object when light from that object travels to your eye. In order to view an object, you must sight along a line at that object; and when you do light will come from that object to your eye along the line of sight. To view the image of an object in a mirror, you must sight along a line at the image. One of the many rays of light from the object will approach the mirror and reflect along your line of sight to your eye.
Reflection
The bouncing back of a light ray from a surface.
Law of Reflection
When a light ray is incident upon a reflecting surface, the angle of reflection is equal to the angle of incidence. Both of these angles are measured relative to a normal drawn to the surface. The incident ray, the reflected ray, and the normal all lie in the same plane.
The Law of Reflection is Always Observed (regardless of the orientation of the surface)
Specular reflection
Reflection off of smooth surfaces such as mirrors or a calm body of water
rays reflect to form a clear image reflected rays are nearly parallel normals drawn to the surface (at the point at which the incident ray strikes the surface) are nearly parallel.
Diffuse reflection
Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway
rays reflect in many directions and no clear image is formed none of the normals drawn to the surface (at the point at which the incident light ray strikes the surface) are parallel.
Types of mirrors: Plane mirrors: flat mirror that reflects light rays in the same order as they approach the mirror.
Spherical mirrors: portion of a sphere that is sliced away and then silvered on one of the sides to form a reflecting surface – two types - concave Mirrors - convex Mirrors
Type of images: 1. Real images - formed by converging light rays; can be projected on a screen; orientation = inverted 2. Virtual images - formed by diverging light rays; cannot be projected on a screen; orientation = upright
PLANE MIRRORS
Characteristics of plane mirror images: 1. Object height = image height 2. Object distance = image distance 3. Always forms a virtual image (cannot be projected onto a screen, behind the mirror, upright) 4. Image is reversed, left to right
Drawing plane mirror ray diagrams:
1. Draw the object and the mirror 2. Draw two incident rays from the object to the mirror 3. Construct the reflected rays -- solid line in front of the mirror, dashed line behind to represent the fact that no light actually reaches the image. 4. Locate the image where reflected rays intersect behind the mirror.
How much of the mirror is needed to view the image?
Examples: CURVED MIRRORS
Concave mirrors - silvered on Convex mirrors - silvered on the inside of the sphere – the outside of the sphere - converging - RRs can converge diverging - RRs diverge (spread (come together) to form a real out) to always form a virtual image or diverge to form a image virtual image
Center of curvature - C - center of the sphere from which the mirror was sliced.
Vertex – Geometric center of the mirror - the point on the mirror's surface where the principal axis meets the mirror.
Focus or Focal Point - F - The point midway between the vertex and center of curvature where parallel light rays converge; the focus is always found on the inner part of the sphere of which the mirror is a small slice.
Principal axis - line drawn through the vertex, focus, and center of curvature of the mirror.
Radius of Curvature – R- The distance from the vertex to the center of curvature - radius of the sphere from which the mirror was cut.
Focal Length – f- distance from vertex of mirror to focal point (f = R/2) Characteristics of concave mirrors:
1. Object and focus are on the same side of the mirror (inside the arc) 2. Focal length is (+) (because the object and the focus are on the same side of the mirror) 3. Real, inverted images are formed when the object is beyond the focal length 4. Virtual, upright images are formed by the mirror when the object is within the focal length 5. No image is formed when the object is at F 6. When the object is at C, an inverted image is formed at C
Concave mirrors can produce either real or virtual images. - when rays from a concave mirror converge, they form a real image. - when rays from a concave mirror diverge, they form a virtual image.
Prediction of image location:
f = focal length (+) do = object distance (+) Image height: di = image distance (+) if real; (-) if virtual hi = image height (+) if upright; (-) if inverted ho = object height (+) m = magnification (<1 if reduced; >1 if enlarged)
Magnification ratio:
Ray Diagrams for Concave Mirrors
Process of drawing ray diagrams is the same no matter where the object is located.
1. IR parallel to the principal axis, RR through the focal point upon reflection.
2. IR through the focal point F, RR parallel to the principal axis upon reflection.
3. IR through C, RR reflects through C.
4. Image is formed at the intersection of RRs.
1. Object located beyond C
2. Object located at C
3. Object located between C and F
4. Object located at F
5. Object located between F and mirror
CONVEX MIRRORS
Characteristics of convex mirrors:
1. The object and the focus are on opposite sides of the mirror (the focus is on the inside of the mirror and the object is on the outside) 2. The focal length is (-) (because the object and the focus are on opposite sides of the mirror) 3. Only virtual, upright, reduced images are formed
Ray Diagrams for Convex Mirrors
Process of drawing ray diagrams is the same no matter where the object is located.
1. IR parallel to the principal axis, RR through the focal point upon reflection.
2. IR through the focal point F, RR parallel to the principal axis upon reflection.
3. IR through C, RR reflects through C.
Convex mirrors always produce upright, reduced, virtual images.
Prediction of image location:
f = focal length (-) do = object distance (+) Magnification ratio: di = image distance (-) hi = image height (+) ho = object height (+) m = magnification (< 1)
Image height:
Focal Image Image Magnification Image Length Location Orientation Type Flat Mirror ∞ -di = do upright 1, same size Virtual Concave, + R > di > f inverted < 1, smaller Real do > R Concave, + di > R inverted > 1, bigger Real R > do > f Concave, + -di upright > 1, bigger Virtual do < f Convex - -di upright < 1, smaller Virtual
The +/- Sign Conventions
The sign conventions for the given quantities in the mirror equation and magnification equations are as follows:
f is + if the mirror is a concave mirror f is - if the mirror is a convex mirror
di is + if the image is a real image and located on the object's side of the mirror.
di is - if the image is a virtual image and located behind the mirror.
hi is + if the image is an upright image (and therefore, also virtual)
hi is - if the image an inverted image (and therefore, also real)