1. Find image with a thin lens
Object ho do hi di F f
Object ho do hi di

2. Analytical calculations
Thin lens equation. ho hi

3. Analytical calculations
Lens maker’s equation:
The formula for a lens in vacuum (air): F
n : index of refraction of
the lens material.
R1 : radius of near surface.
R2 : radius of far surface.
far surface
near 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.

4. Analytical calculations
Lens maker’s equation:
The formula for a lens (nlens) in medium nmedium : F
near surface
far surface
nmedium
R1 : radius of near surface.
R2 : radius of far surface.

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 is defined to be:

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

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

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. Nearsightedness (myopia):
Vision corrections
Nearsightedness (myopia):

13. Farsightedness (hyperopia):
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?
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.
So the contact lens is a diverging lens with a focal length of 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.
2.00 cm
Far point
Near point = 15.0 cm. The image distance has to be -(15.0 – 2.0) cm = 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 cm.

16. Two lenses − objective and eyepiece Objective focal length very short
Multiple lens system
Microscope:
Two lenses −  objective and eyepiece
Objective focal length very short
First image real, near eyepiece focal point
Final image inverted, magnified, virtual
Angular magnifying power is

17. The magnifying power of a microscope
M = overall magnification
mob = objective lateral magnification
Mey = eyepiece angular magnification
L = distance between the lenses
N = near point distance of your eye
fob = focal length of objective
fey = focal length of eyepiece

18. Focal points at same location
Multiple lens system
Telescope
Two converging lenses
Focal points at same location
Final image inverted, at infinity, virtual
Angular magnifying power is

19. The magnifying power of a refracting telescope
Image inverted