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Lenses

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Objective of the lesson: Having covered refraction, we can use our knowledge to discuss lenses.

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Where are they?
Lenses are used to change the direction of light (based on refraction). They are used in cameras, optical telescopes, microscopes…

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Convex lenses
The lens below is called a convex lens. It is fatter in the middle and magnifies images. The image will be upside down.

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Concave lenses
The lens below is called a concave lens. It is thinner in the middle and gives a small upright image.

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Real Images
Concave mirrors and convex lenses create images by converging the light in a point.

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Virtual Images
Convex mirrors and concave lenses can make it seem as if that the light rays appear to emanate from the virtual image.

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Images, Which is Which?

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The Thin Lens Equation
If an object is placed in the distance a from a lens with focal length f, the image will appear at the distance b from the lens:
Convex (concave) lenses have positive (negative) focal lengths.
Discuss what happens to b, when a is increased based on the formula above.
How far away must the object be for b to be equal to the focal length?

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The Thin Lens Equation
Calculate the focal length of a lens, for which the distance to the image is 2 m, when the distance to the object is 3 m.
Calculate the focal length of a lens, for which the distance to the image is 5 m, when the distance to the object is 3 m.

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The Human Eye

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The Human Eye
Some people need glasses to adjust their eysight, as their eyeballs are too short or too long.

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Glasses
Glasses help you by creating virtual image of the object. So imagine that anything that is further away than 1 m seems blurry to you, then your glasses will make it “look like the object is no further away than 1 m”. Consequently, we need the lens equation, describing images:

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Myopic
Here’s an example: Bob needs glasses. Anything beyond 85 cm seems a bit blurry to him. Assume that Bob would like to be able to focus on objects as far away as the weather will allow (objects at infinity).
We use the thin lens equation:
So Bob needs a lens with a focal length of -0,85 m
What lens would Bob need, if anything further away than 40 cm seemed blurry?

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Hyperopic
Here’s an example: Bob needs glasses. Anything closer than 35 cm seems a bit blurry to him. Assume that Bob would like to be able to focus on objects that are 20 cm away.
We use the thin lens equation:
So Bob needs a lens with a focal length of 0,47 m.

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Diopters
This is how the optometrist will give the prescription. The power of a lens (units are called DIOPTERS) is just the reciprocal of the focal length, in meters. Thus a lens with a power of +0.5 diopters will have focal length 2 meters. So Bob needs a lens with a focal length of -0,85 m, he needs
Calculate the powers of lenses with focal lengths of m, m, -0,1 m and -1.4 m in Diopters. Is the person hyperoptic or myoptic?