Today 2/7 Diverging Lenses--Ray Diagrams and Math HW Questions? Start reading chapter 26.6-8 on Lenses HW: “2/7 Diverging Lens” (three pages)

Due Wednesday 2/12 Exam I Thursday, Feb 13

Lenses -- Wave Picture

A converging lens bends light toward the axis

Converging Lenses

Focal point is the place on the axis where all rays arriving parallel to the axis are directed

There is a second focal point on the input side where all rays directed away from it leave parallel to the axis

“In through focus-out parallel” “In parallel-out through focus”

focal lengthfocal length

Converging Lens-Ray Diagrams

ff

d0 object distanceimage distance di

Now we have to “backtrack” the rays to see where they seem to come from!

f = +4cmd0 = +2cmdi = -4cmh0 = +1cmhi = +2cmm = +2 (no units)

Equations

fdd i

111

0

Thin lens equation

00 d

d

h

hm ii Magnification equation

f focal length always + for converging lens (- for diverging)d0 object distance + if on input sidedi image distance + if output side (- if on input side)m magnification + if image is (- if image inverted)h height + if not inverted (- if inverted)

Lenses -- Wave Picture

A converging lens bends light toward the axis

A diverging lens bends light away from the axis

Lenses -- Wave Picture

A converging lens bends light toward the axis

Focal point is a place on the axis where all rays directed parallel to the axis arrive

Lenses

A diverging lens bends light away from the axis

Now the Focal point is a place on the axis where all rays directed parallel to the axis seem to come from

Lenses

Now the Focal point is a place on the axis where all rays directed parallel to the axis seem to come from

There is a second Focal point on the axis. Any ray directed toward it from the far side are directed parallel to the axis.

Diverging Lens-Ray Diagrams

ff

Bend the ray at the middle of the lensIn parallel-out as if from left focus

Also straight through the center of the lens

For lenses (both types) di is positive on the right.Here di will be a negative number. f is negative for diverging lenses.

di

In as if toward right focus-out parallel

Diverging Lens-Ray Diagrams and Math

ff

di

d0 = +12 cm, f = -4 cm find di, m, hi

fdd i

111

0

00 d

d

h

hm ii

Virtual and Real Images

Real: Virtual:

A screen placed at the image will produce an image.

A screen placed at the image will not produce an image.

All image forming rays actually pass through the image.

At most only one image forming ray will pass through the image.