With Lenses

Created by Derek J. Wells. Under the expressed written consent of Derek J. Wells in accordance with the rules and by-laws of Derek J. Wells. All events depicted here are fictional. Any similarity to real life situations are merely coincidental.

What Do Lenses Do ??When light passes through a Lens, it is refracted (bent). This bending of light produces an image of the object that is different from it original appearance.Objects viewed through lenses produce images that vary based on where the object is located and on the type of lens that is used.

There are two types of lenses.

A converging lens. And A diverging lens

This is also called a convex lens because the surface of the lens has a convex shape.

This is also called a concave lens because the surface of the lens has a concave shape.

This lens looks like a “cave” if you were walking into it.

The converging lens causes horizontal light rays to converge (come together) when it hits.

The diverging lens causes horizontal light to diverge (move apart) when it hits.

Terminology

Principle Axis = The horizontal line drawn through the center

f = Convex lens Focal point = the point through which all horizontal rays hitting the lens pass through when they refract (bend)

f = Concave lens Focal point = the point at which all horizontal rays hitting the lens appear to come from when they refract (bend)IMPORTANTThese focal points are negative (-)In the diverging lens

Point 2f is twice the focal point and is used as a reference point in a lens problem

f f2f 2f f f2f 2f

Terminology Continued ...

f f2f 2f

An object placed near a lens

The image of the object that is produced by the lens

d0

Distance object is placed from the lens center

di

Distance image is formed from the lens center

Front Side of Lens(the virtual side)

Back Side of Lens(the real side)

When images are formed on the front side of the lens they are virtual images. When you look through a lens and the object looks different than usual you see a virtual image (such as a magnifying glass)

When images are formed on the back side of the lens they are real images. Real images can be projected onto a screen.

Also

ho = object height

hi = image height

iddf

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d

dM

Determining the Image

di = (+) real imagedi = (-) virtual imageM = (+) uprightM = (-) inverted (upside down) | M | = 1 same size| M | < 1 smaller| M | > 1 larger

note | M | = (absolute value of M)

Lens EquationsLens Equations - You can find out where and what an image should look like by using the lens equations

To find the distance of the image from the lens

To find the Magnification and Orientation of the Image

Important - when using a diverging lens the focal point (f) must be made negative (-)

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h

hM

Convex lenses can form any types of these images - real or virtual - smaller, same size, or larger - inverted or upside down

Concave lenses can only form one type of image ALWAYS

- smaller, upright, virtual

id

1

8

1

4

1

id

1125.025.0

id

1375.0

8

) 67.2( cmM

Example: A concave lens with (f = 4 cm, d0 = 8 cm)

iddf

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0

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cmdi 67.2

Note that the f is (-) since it’s a concave lens

33.0M

di = (-) so its virtual

M = (+) so its (upright)

| M | < 1 so its smaller

2f f 2ff

Ray Diagrams (for convex lenses)We use ray diagrams to draw a picture of what the image would look like

3 Light rays are drawn all originating from the tip of the OBJECT. The point where these rays intersect gives the location where the tip of the IMAGE will be

Lets try an example with f = 5 cm, do = 12 cm

The first light ray we draw goes through the center of the lens

This light ray passes through unaffected and keeps going the same way

2f f 2ff

Ray Diagrams (for convex lenses)

The second light ray we draw goes horizontally towards the lens and stops in the center of it (the light actually bends the whole time its in the lens, but as a convention we make it bend when it hits the center.

This light bends and passes through the focal point on the other side of the lens

2f f 2ff

Ray Diagrams (for convex (CONVERGING) lenses)

The last light ray we draw goes through the focal point on the front side at stops at the center of the lens

This light ray bends and emerges horizontal on the back side

image

Describe the image:

Real

Inverted

Smaller

2f f 2ff

A convex lens (converging) with (f = 2 cm, d0=5 cm)

iddf

111

0

id

1

5

1

2

1

id

12.05.0

Check the math

id

13.0 cmdi 33.3

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d

dM

67.0 5

33.3

M

di = (+) so its real

M = (-) so its inverted

| M | < 1 so its smaller

Putting it all together.Draw all three rays and the point where they intersect represents the point where the tip of the image will be formed

Describe the image:Virtual

Upright

Larger

2f f 2ff

Lets try - A convex lens with (f = 2 cm, d0=1 cm)

Special Examples (For Convex Lenses)1- When the object is located exactly on (f) the rays will not intersect anywhere and there will be no image

2- When the object is placed in front of (f) the rules are a little bit different

Notice the rays do not intersect on this side. So we have to extend these refracted rays back to the front of the lens to see where they appear to come from

The intersection of the extensions through the lens show you where the tip of the image will be formed

The first two rays are the same as before

The third ray cannot be drawn through (f) since we are in front of it so it is drawn as if it originated at (f), and this ray refracts horizontal after hitting the center.

Image

2f f 2ff

Ray Diagrams (for concave (DIVERGING) lenses)The nice thing about Concave lenses is that the ray diagrams are ALWAYS,

ALWAYS the same. They are slightly different then the convex lenses however and you should be careful to notice the differences. In this type of lens, you always have to extend the refracted rays back behind to find the image

Lets try an example with f = 5 cm, do = 12 cm

The first light ray we draw goes through the center of the lens

This light ray passes through unaffected and keeps going the same way

2f f 2ff

Ray Diagrams (for concave lenses)

The second light ray we draw goes horizontally towards the lens and stops in the center of it

This light bends as if it came from the focal point on the front of the lens

2f f 2ff

Ray Diagrams (for concave lenses)

The last light ray we draw goes TOWARDS the focal point on the other side and stops at the center of the lens

This light ray bends and emerges horizontal on the back side

Describe the image:

Virtual

Upright

Smaller

2f f 2ff

A concave lens (diverging) with (f = 2 cm, d0=5 cm)

Remember when doing the math (f = (-)).. The math for this lens will always show

di = (-) so its virtual

M = (+) so its upright

| M | < 1 so its smaller

Putting it all together.Draw all three rays and extend the refracted rays back behind the lens. The point where the extensions meet is the image point Rays don’t intersect over

here so they are extended back to the front of the lens

Image

Chromatic AberrationWhite light is made up of all the difference colors of light (frequencies).

When light passes through glass, it slows. This slowing causes the light to bend which is why we get refraction. Each of the different frequencies in light bend a little differently and come out at different angles. This phenomenon is known as Dispersion and is how a Prism produces the rainbow colors when light enters it.Since each of these frequencies bend a little differently they fall at the focal point in slightly different spots and can cause a distorted image (example will be shown below). This is corrected with the use of color filters or multiple lenses.

f f2f 2f

Incoming white light

Red light bends less than blue light

Red light bends less than blue light

They are slightly off from the focal point

Glasses and ContactsAn eyeball is a lens. Light bends when it hits it. In a normal eye, light hits

the eye lens, bends and focuses right exactly back on your retina to make an clear image.

Your eye can be slightly misshapen from strain and this can cause the light not to focus on your retina.

When light bends too much it focuses before it hits your retina and you are nearsighted and this is called MYOPIA

When light does not bend enough it focuses behind the retina and you are farsighted. This is called HYPEROPIA

Fixing the problemWith MYOPIA light bends too much so we need to bend the light out a little before it hits the eye. We want the light to diverge a little so we put a diverging lens in front

With HYPEROPIA light bends too little so we need to bend the light in a little before it hits the eye. We want the light to converge a little so we put a converging lens in front

AN IMPORTANT Side Note.

- These equations and rules apply to THIN lenses in air. When lenses are thicker or they are placed in other substances like water, the focal points change and the math becomes more advanced.

Experimental Laboratory Optics

-Image formation using real lenses can be performed in class labs.

- Using a candle, an image can be projected onto a piece of paper that is moved into the proper location to find the focused image.

- A ruler can be used to measure image and object distances and the focal point of the lens can be calculated, or if the lens focal point is known, we could determine an experimental value

Experimental Laboratory Optics … continuedNote: in these labs, the objects are not very far from the lenses so the images will form in various locations based on object distance to the lens.

IMPORTANT: Light traveling a far distance to a lens is assumed to be all horizontal relative to the lens. For this situation, all of the light will converge to the focal point and the image will only be found directly at the focal point

- This is a handy way to estimate the focal point of a lens, by focusing an image of a tree far away on a piece paper, or even better, by focusing an image of the sun on a card, we know that the location of that image must be at the focal point of the lens. When you start fire with the sun and a lens, you are essentially making an image of the sun to burn the paper.

Fini

That’s the end of the lenses presentation. If you enjoyed this film, look for other great

presentations such as”How To Get Good Grades in

Physics with $100 bills ”

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