What is Geometric Optics
It is the study of light as particles.
Geometric optics treats light as particles (or rays) that travels in straight lines.
Physical optics (wave optics) deals with the wave nature of light, such as the spreading of waves (diffraction) and the interference of waves.
Some notationsF: focal pointO: objectI: image
f: focal lengthi: image distancep: object distance
Principle axis
Your textbook:f: focal lengths': image distances: object distance
Converging Lens (thin)
Rules:1. Rays parallel to axisPass through focal point2. Rays through focal pointPass parallel to axis3. Rays through the centerPass through unaffected
In fact all light rays from the object pass through
the image
You only need two rays to find the image
Real and Virtual ImageReal image can be projected directly on a screen.Virtual image cannot be projected directly on a screen without extra lenses or mirrors.
Real image forms when rays actually converge and meet.Virtual image forms when rays diverge and do not meet. Position of a virtual image is found by tracing the rays backward.
The sign of ii is positive if the image is on the righti is negative if the image is on the left
i >0 i<0
SolutionAssume f = 1m, complete the table below.
p i m
∞ 1 0
3 1.5 -0.5
2 2 -1
1.5 3 -2
1 ∞ ∞
0.5 -1 +2
Diverging Lens (thin)Rules:1. Rays parallel to axisPass through focal point2. Rays through focal pointPass parallel to axis3. Rays through the centerPass through unaffected
Negative fDiverging lens obeys the lens equation too. Except that f is now negative.
2cm
Example:f =-2cm
The typical case for concave lens
For concave lens, the image is always virtual and upright, no matter where the object is.
Example: Diverging LensYou are given a diverging lens of focal length 20cm. You
want to form an virtual image that is 1/3 the height of the object. Where should the object be placed?
Confusing signsConvergin
gLens
DivergingLens
Converging
Mirror
Diverging
Mirror
Other name
ConvexLens
ConcaveLens
ConcaveMirror
ConvexMirror
f + - + -
i when image is on
the left- - + +
i when image is on
the right+ + - -
Lensmaker’s EquationProof not required. No need to memorize, will be given in the exam. One question in Mastering Physics.R>0 if convex (bulging) toward the object.
Curved MirrorsConcave mirrorConverging mirrorPositive mirror
Convex mirrorDiverging mirrorNegative mirror
Only one focal point for curved mirrors
A lens has two focal points (one on each side of the lens), but a curved mirror only has one focal point. It is important to remember where they are.Concave mirrors: F in front of the mirrorConvex mirrors: F behind the mirror
Concave Mirror Rules
F
Rules:1. Rays parallel to axisReflect through focal point2. Rays through focal pointReflect parallel to axis3. Rays through the centerReflect with equal angle
Really the same rules as converging lens
Convex Mirror Rules
F
Rules:1. Rays parallel to axisReflect through focal point2. Rays through focal pointReflect parallel to axis3. Rays through the centerReflect with equal angle
Really the same rules as diverging lens
Lens Equation applies
f is positive for concave mirrorf is negative for convex mirror
i is positive if image is in front of the mirrori is negative if image is behind the mirror
Convex mirror
For convex mirror, the image is always virtual and upright, no matter where the object is.
Multiple lensesIn the case when the first lens form a image in front of the first lens, simply treat the image as the object for the second lens.We will skip the case when the first lens gives an image behind the second lens.
Example: Image of an imageAn object 8cm high is placed 12cm to the left of a
converging lens of focal length 8cm. A second converging lens of focal length 6cm is placed 36cm to the right of the first lens. Find the position and size of the final image.
Virtual Objecthttp://science.sbcc.edu/~physics/flash/optics/virtualobject.html
p is negative for virtual objects
Confusing signsConvergin
gLens
DivergingLens
Converging
Mirror
Diverging
Mirror
Other name
ConvexLens
ConcaveLens
ConcaveMirror
ConvexMirror
f + - + -
i when image is on
the left- - + +
i when image is on
the right+ + - -
Summary
Both equations are true for lens and mirrors, but you have to be very careful about the signs!
Area of view and focal length Longer focal length, the less light is collected, need
to compensate by increasing the diameter of the aperture D. You want to keep the “f-number” f/D constant for the same intensity.