1

Find image with a thin lens

F

F

fObject

hodo

hi

di

F

Ff

Object

hodo hi

di

2

Analytical calculations

Thin lens equation.

fdd oi

111

o

i

o

i

d

d

h

hm :ionmagnificat

ho

hi

3

Analytical calculations

Lens maker’s equation:

The formula for a lens in vacuum (air):

21

111

1

RR)n(

f

n : index of refraction of the lens material.R1 : radius of near surface. R2 : radius of far surface. The near or far surface is with respect to the focal point F. Near

side is surface 1, far side is surface 2. The sign of the radius is then defined as

“+” if the center is on the far side; “-” if the center is on the near side. In this convention, positive f means converging lens, negative f means diverging lens.

F

near surface

far surface

4

Analytical calculations

Lens maker’s equation:

The formula for a lens (nlens) in medium nmedium :

21

111

1

RR)

n

n(

f medium

lensR1 : radius of near surface. R2 : radius of far surface.

F

near surface

far surface

nmedium

5

Sign convention table

6

Angular size

The height of an object is measured by a meter stick. The height of the same object we see through our eyes depends on the how far away the object is to our eyes.

7

Angular size

Angular size is defined to be:

d

h

8

Angular magnifying power

Angular magnifying power: the ratio of the image angular size over the object angular size.

0

M

9

Human eyes

The human eye is modeled in physics as a simple thin lens system with a fixed image distance, but the focal length can change in a range.

di)( maxmin f,ff

10

Human eyes

The focal length range correspond to a person’s near point and far point:

Near point: when the object is pushed as close as one can have clear image. This is the point when the eye’s focal lens is at its minimum value.

11

Human eyes

The focal length range correspond to a person’s near point and far point:

Far point: when the object is pushed as far as one can have clear image. Optically this is the point when the eye’s focal lens is at its maximum value. For healthy eyes, this far point is usually almost at infinity.

12

Vision corrections

Nearsightedness (myopia):

13

Vision corrections

Farsightedness (hyperopia):

14

Vision correction examples

Refractive power: The reciprocal of the focal length. Often used by opticians and optometrists, who specify it in diopters (unit: 1/m).

Nellie is nearsighted. She cannot focus on objects farther than 40.0 cm from her unaided eye. What focal length must her corrective contact lens have to bring into focus the most distant objects?

fP

1

Far point = 40.0 cm, a correcting lens needs to generate the image of an object at infinity at this far point for her to see clearly. Contact lens means the correcting lens and the lens in the eye has zero distance between them.

cm040.fc

So the contact lens is a diverging lens with a focal length of -40.0 cm.

15

Vision correction examples

Elizabeth is nearsighted. Without glasses, she can see objects clearly when they are between 15.0 cm and 90.0 cm away from her eyes. Her glasses are designed to be worn 2.00 cm from her eyes, and have a focal length so that objects at infinity produce images at her far point. When she is wearing these glasses, how close to her eye can an object be before it appears out of focus?

Far point = 90.0 cm, near point = 15.0 cm. A correcting lens needs to generate the image of an object at infinity at this far point minus the 2.00 cm for her to see clearly. Contact lens means the correcting lens and the lens in the eye has zero distance between them.

cm088.fc

2.00 cmFar point

Near point = 15.0 cm. The image distance has to be -(15.0 – 2.0) cm = -13.0 cm of an object placed at the new near point with the correcting lens. Use the lens equation to find this new near point to be 15.25 cm.

16

Multiple lens system

Microscope:

Two lenses −  objective and eyepieceObjective focal length very shortFirst image real, near eyepiece focal pointFinal image inverted, magnified, virtualAngular magnifying power is

 

0

0

M

17

The magnifying power of a microscope

eyeob

eyeob

ff

LNM

MmM

M = overall magnificationmob = objective lateral magnification

Mey = eyepiece angular magnification

L = distance between the lensesN = near point distance of your eyefob = focal length of objective

fey = focal length of eyepiece

 

18

Multiple lens system

Telescope

Two converging lensesFocal points at same locationFinal image inverted, at infinity, virtual

Angular magnifying power is

 

0

0

M

19

The magnifying power of a refracting telescope

eye

ob

ob f

fM

Image inverted