Understanding Focal Points in Optics, Slides of Optics

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Focal Points

Basic Optics, Chapter 4

Focal Points

 Every spherical lens has 2 focal points:

 Primary focal point

 Secondary focal point

Focal Points: Primary

 Primary focal point: Location at which an

object could be placed, and light rays

associated with the object would exit the

lens with zero vergence (i.e., parallel)

 In terms of the Vergence Formula, this means that

V = 0, and therefore U and P are of equal-but-

opposite magnitude

U + P = V

U + P = 0 These have to be the same value, with one of them (-), in order for them to sum to zero

Focal Points: Primary

Primary Focal Point

Parallel rays to infinity (vergence = 0)

U + P = 0

Focal Points: Secondary

 Secondary focal point: Location at which the

image is formed when light rays with zero

vergence (i.e., parallel) encounter a given lens

Focal Points: Secondary

 Secondary focal point: Location at which the

image is formed when light rays with zero

vergence (i.e., parallel) encounter a given lens

 In terms of the Vergence Formula, this means that

U = 0, and therefore P equals V

U + P = V

0 + P = V

P = V

Focal Points: Secondary

Parallel rays from infinity (vergence = 0)

Secondary Focal Point

0 + P = V

Focal Points

 Note:

 Primary focal points are object locations; secondary focal points are image locations

Object

Object

Image

Image

Primary focal point

Secondary focal point

Focal Points

 Note:

 Primary focal points are object locations; secondary focal points are image locations  For each lens type, primary and secondary focal points are on opposite sides of the lens  For plus vs minus lenses, the position of the primary and secondary focal points are reversed

Object

Object

Image

Image

plus lens but right of the minus lens^ Primary^ focal point is to the left of

Secondary of plus lens but left of the minus lens focal point is to the right

Focal Points

 Note:

 Primary focal points are object locations; secondary focal points are image locations  For each lens type, primary and secondary focal points are on opposite sides of the lens  For plus vs minus lenses, the position of the primary and secondary focal points are reversed  Primary and secondary focal points are NOT conjugate points

Object

Object

Image

Image

Focal Points

 Conjugate points : Two points that are object

and image of one another

Focal Points

A

-.5 meters

P = +

Object U =?

 Conjugate points : Two points that are object

and image of one another

U + P = V

Focal Points

A

-.5 meters

U = -2 V =?

P = +

U + P = V

Object

 Conjugate points : Two points that are object

and image of one another

Focal Points

A

-.5 meters

U = -2 V = +

P = +

U + P = V

Object

 Conjugate points : Two points that are object

and image of one another