Lab 9: Geometrical opticsOnly 3 more labs to go!!

Today we are going to do three experiments:

1. Measure the intensity of light as a function of distance away from its source.

2. Measure the focal length of a lens

3. Measure focal length of a mirror

Light intensity (sometimes called illumination is defined as the amount of light energy falling on a certain area.

The intensity of light from a source depends on two things: 1. The source (I.e. Laser vs. a candle)2. The distance you are away from the source

The equation for intensity is:

where is the amount of light energy emitted from the sourceand r is the distance you are away from the source

24 rI

I

r

NOTE: The intensity is directly proportional to the power of the source but inversely proportional to the SQUARE of the distance

mxby

rI

ln2)4ln(ln ln I

ln r

y-int = ln( 4) slope = 2

Mirrors: When light encounters a mirror it gets reflected. According the LAW OF REFLECTION the angle of reflection equals the angle of incidence

FLAT MIRROR

I R R = I

The LAW OF REFLECTION still holds true if the mirror has some shape to it. Look at thisDIVERGING MIRROR (or sometimes called a CONVEX MIRROR)

R = I

Notice that if trace the reflectedlight rays back they seem to originatefrom a point behind the mirror. For this reason images viewed with divergingmirrors are always upright, smaller, and“virtual”

Furthermore this focal length is relatedto the radius of curvature of the mirrorby:

2

rf

Converging mirrors (sometimes called concave) are opposite to diverging mirrors, they cause light raysto converge to a focus.

The type of image this mirror produces depends on the position of the object relative to the focal point

LENSES:

LENS

I R

t

When light encounters something transparent some of thelight will be reflected as before. However, most of it willenter the transparent object and be refracted, or “bent”.

Lenses allow light to enter the glass and be bent. If the transparent media is curved then we willhave a lenses.

If the lens is thinner in the middlethan at the edge, then it is a diverging lens

The lens will diverge parallel light rays. The imageviewed with a diverging lens will always be virtual,smaller, and upright.

Diverging Lens

Converging Lens If the lens is made such that it is thicker in themiddle this will be a converging lens.

This lens will focus incoming light rays to a point.

Ray tracing with lenses:

Object

X Xf f

1st: Draw a line through the middle lens 2nd :Draw a line parallel to axis and make it pass through the focal point

X Xf fNotice how these rays never

intersect. In this case you must the original rays backwards.

Converging Lens

Real Object Side (+)

Real Image Side (+)

Virtual Object Side (-)

Virtual Image Side (-)

Virtual Image Side (-) Real Image Side (+)

Real Object Side (+) Virtual Object Side (-)

Ray tracing with lenses:Diverging Lens

X Xf f

1st: Draw a line through the middle lens2nd :Draw a line parallel to axis and make its projection pass through the focal point

X Xf f

Len’s makers equation:foi

111 here, i is the image distance, o is the object

distance and f is the focal length.

NOTE: If, i, o are on their VIRTUAL SIDES they will be negative. Let’s look at an example:

An object 3 cm high is placed 15 cm in front of a converging lens of 10 cm focal length.Where is the image located?

Since this is a converging lens and the object is outside the focal length we know that the imageformed will be a REAL IMAGE, so is will be positive. So we use the len’s maker’s equation to solvefor i.

cmicmi

cmcmcmcmofifoi

3030

11

30

2

30

3

15

1

10

1111111