1. Compound Lens

2. Two Lenses A single convex lens produces a real image.
That image can be acted on by a second lens.
Second image can be real or virtual

3. Final Image
Two thin convex lenses with focal lengths 0.30 m and 0.50 m are separated by 0.20 m.
An object is placed 0.50 m in front of the first lens.
Find the image in the second lens.
First apply the lens equation to the first lens.
f1 = 0.30 m, so1 = 0.50 m
The intermediate image is so2 = 0.75 – 0.20 = 0.55 m beyond the second lens.
f2 = 0.50 m, so2 = m
This is a real image

4. Touching Lenses Two lenses are often brought into close contact.
Very short distance between optical centers
The combined focal length can be approximated.
Let so1 approach infinity
Applies to convex and concave lenses

5. Farsighted Some eyes have weak muscles.
Near image focuses in front of the retina
Hyperopia and presbyopia
A compound converging lens compensates for the eye’s lens.
Forces the image forward in the eye.

6. Nearsighted Some eyes have eyes too long or bent corneas.
Distant image focuses in front of the retina
Myopia
A compound diverging lens forces the image back in the eye.
Pinhole iris or squinting also works

7. Diopters Optometrics works on corrective lenses for eyes.
Diopters measure the inverse of the focal length of the lens.
1 D = 1 m-1
Positive converging
Negative diverging

8. Reading Glasses
A person sees blurred print at 25 cm, but is fine at 125 cm.
Find the diopter correction needed.
The diopter formula can be applied to object and image distances.
Object is at 0.25 m
Virtual image is at 1.25 m
Correction needed is +3.2 D
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