Light and Optics Mirrors and Lenses

Types of Mirrors Concave mirrors – curve inward and may produce real or virtual images. Convex mirrors – curve outward and will always produce a virtual image. Flat mirror – always produces a virtual image.

Types of Images for Mirrors Real Image – is always inverted and may be smaller, larger, or the same size as the object. Always forms on the same side as the object Virtual Image – always forms behind the mirror and is always upright and reduced.

Finding the Focal Point of a Concave Mirror If the light source is ‘infinitely’ far away, the rays of light are parallel to each other and pass through the Focal Point. The distance from the mirror to F is the focal length.

The center of Curvature C is always twice the distance of F or F is ½ the center of curvature. The line that runs through the middle or the mirror is called the Principle Axis.

Terms for both mirrors and lenses Terms: d o = object distance ( how far from the mirror or lens the object is) d i = image distance ( how far from the mirror or lens image will be) + d i = real image - d i = virtual image h o = the object size h i = image size ( how tall the image will be) - h i = real image (inverted) + h i = virtual image (upright) m = magnification (how much the image will be enlarged or reduced)

Ray 1 ray 2 With a ruler, draw ray 1 parallel to the principle axis to the mirror Draw ray 2 from the tip of the object through the Focal Pt. to the mirror. Ray Drawings for a Concave mirror

Ray Drawings for a Concave Mirror ray 1 ray 2 Using a ruler, draw a ray 1 from the mirror down through F. Ray 2 is drawn from the mirror outward parallel to the principle axis.

Ray Drawings for a Concave Mirror Where the 2 rays cross, the image will form. It is inverted, reduced, and forms between C and F

Convex Mirrors F and C are behind the mirror, the object is in front of the mirror, this makes F and C negative values.

Convex Mirrors A convex mirror will always produce a virtual image because the rays of light never converge.

Ray Drawings for a Convex Mirror object Ray 1 Ray 2 Using a ruler, draw a line from the tip of the object, parallel to the principle axis, to the mirror. Ray 2 is drawn by placing a ruler on the tip of the object and lining it up with the Focal point behind the mirror.

Ray Drawings for a Convex Mirror object ray 1 ray 2 Place a ruler where ray 1 strikes the mirror and line it up with the Focal point. Draw a line going away from the mirror. Next, place the ruler where ray 2 strikes the mirror and draw a line away form the mirror, parallel to the principle axis.

Ray Drawings for a Convex Mirror Extend backwards with dotted lines ray 1 and ray 2 until they cross behind the mirror. The image is upright, reduced, and virtual. ray 1 ray 2

Types of Lenses Convex lenses curve outward and may produce real or virtual images. Concave lenses curve inward and always produce a virtual image.

Types of Images for Lenses Real images are always inverted and form on the opposite side of the lens. They may be reduced, the same size, or enlarged. Virtual images are always upright and form on the same side of the lens as the object. They are always reduced.

Converging or Convex Lens There is a Focal point on each side plus a 2F point on each side. There is no C (center of curvature, but 2F has the same relationship)

Ray Drawing for a Convex lens Draw ray 1 from the tip of the object to the center of curvature of the lens. Draw ray 2 from the tip through the center of the lens on the principle axis and continue to draw the line. Draw ray 3 from the tip through F on the same side to the center line ray 1 ray 2 ray 3

Ray Drawing for a Convex lens Draw ray 1 from the center through the opposite F. Ray 2 is already drawn. Ray 3 is a parallel line drawn form the center of the lens. Where all 3 rays cross, the image will form. ray 1 ray 3 ray 2

How the total image is formed.

Concave Ray Diagram Draw ray 1 parallel to the principle axis and then line up the ruler with that point and f 1. Continue the line out of the lens.

Concave Ray Diagram Draw ray 2 by placing the ruler at the tip of the object and the focal point on the other side of the lens (f2)

Concave Ray Diagram Draw ray 3 by placing the ruler at the tip of the object and the point where the principle axis meets the center of curvature. It is a straight line because it does not refract.

Concave Ray Diagram Since none of the lines converge, draw back through the lens with dotted lines until they converge. This is where the virtual image will form. It will be upright and reduced.

Terms for both mirrors and lenses Terms: d o = object distance ( how far from the mirror or lens the object is) d i = image distance ( how far from the mirror or lens image will be) + d i = real image - d i = virtual image h o = the object size h i = image size ( how tall the image will be) - h i = real image (inverted) + h i = virtual image (upright) m = magnification (how much the image will be enlarged or reduced)

Mathematical Formulas for both mirrors and lenses d i = f d o d o – (f) (the quantity f can be + or – ) h i = -(d i )h o (the quantity d i can be + or -) d o f = d o d i d o + d i m = h i = -d i (if m is negative, it is reduced) h o d o (if m is positive, it is enlarged)