Reflection and MirrorsThe Law of Reflection always applies:

“The angle of reflection is equal to the angle of incidence.”

“Plane” Mirrors form virtual images.

Virtual: light APPEARS to come from this location, but does not actually start there.

The image is the same distance behind the mirror as the object is in front of the mirror.

The image is the same size as the object.

If you wish to take a picture of your image while standing 2 meters in front of a plane mirror, for what distance should you set your camera to provide the sharpest focus?

Since the image is the same distance BEHIND the mirror as the object is in front of the mirror….

Set the distance for 4 meters

How big does a mirror have to be in order for you to see your entire image?

Concave Mirrors

*Form “real”, inverted (upside down) images are formed UNLESS the object is inside the focal length…

…Then the images are “virtual” and upright!

Convex Mirrors

The image is always smaller, upright, and virtual-

an SUV.

Used in security cameras and rear-view mirrors in your car.

Focal point

Measurements with mirrors

f - focal length

do – distance from the mirror to the object being observed.

di – distance from the mirror to where an image is formed

m- magnification- compares the size of the object being observed and the image formed by the mirror.

The Mirror Equation

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Where f is the focal length, do is the distance from the mirror to the object, and di is the distance from the mirror to the image.

Magnification

The magnification provided by a mirror is given by

Where hi is the height of the image and

ho is the height of the object

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Yep, it’s time for you to try one…

A concave mirror has a radius of curvature of 15.0 cm. A 1.5 cm tall gummy bear is placed 19.0 cm from the mirror. Where will the image be formed? What is the magnification? How tall is the image?

First find the focal length. f = ½ Rf = 7.5 cm

Now solve for di using the mirror equation.

di = 12.39 cm

Now, get the magnification, m = -di / do

m = - 0.65 it’s negative because the image is inverted.Now for the height of the image: m = hi / ho

hi = -0.98 cm

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Concave and Convex LensesLight REFRACTS as it

passes through lenses, forming images.

Convex lenses are CONVERGINGlenses

Concave lenses are DIVERGING lenses

Refraction: the change in direction as a wave passes from one medium into another

Measurements with lenses

f - focal length

do – distance from the lens to the object being observed.

di – distance from the lens to where an image is formed

m- magnification- compares the size of the object being observed and the image formed by the lens.

Convex Lenses

The “focal length” will be ½ the “radius of curvature”.

Images formed by Convex lensesIf the object is beyond twice the focal length, the image is smaller, inverted, and real- if a piece of paper was placed at the image location, you would see the image on the paper.

If the object is placed at exactly twice the focal length, the image will be exactly the same size as the object, inverted, and real

If the object is placed exactly at the focal point, the light rays are perfectly parallel, and NO image will be formed!

If the object is placed within the focal length, the image will be larger, upright, and VIRTUAL.

NO image would appear on a paper screen placed at the image location!

“Virtual”A “virtual” focal point- real light waves would appear to converge at that point, but they actually do not. Concave lenses have a virtual focal point. Convex lenses have a real focal point.

A “virtual” image- No real image will appear on a screen. The light rays that reach your eye just behave as if they came from the image position

Your Eye

Magnifying glasses

Magnifying glasses are convex lensesthat converge the light towards a focal point

Diverging Lenses

Concave (diverging) lenses ALWAYS form smaller, upright, virtual images.

SUV

People who are near-sighted can see up close but not far away.

They use concave (diverging) lenses, which will make something far away look like it’s up closer.

People who are far-sighted use convex (converging) lenses that make near objects look as if they are further away.

The Lens/Mirror Equation

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Where f is the focal length, do is the distance from the mirror or lens to the object, and di is the distance from the mirror or lens to the image.

Magnification

The magnification provided by a lens or mirror

Where hi is the height of the image and

ho is the height of the object

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Yep, it’s time for you to try one…

A convex lens has a radius of curvature of 8.0 cm. A 12 cm tall troll is placed 7.0 cm from the lens. How far from the lens should a screen be placed in order to have a sharp image? What is the magnification? How tall is the image?

First find the focal length. f = ½ Rf = 4.0 cm

Now solve for di using the lens equation.

di = 9.33 cm

Now, get the magnification, m = -di / do

m = - 1.33 it’s negative because the image is inverted.Now for the height of the image: m = hi / ho

hi = -16 cm

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Using the lens equation for concave lenses

The focal point is VIRTUAL, so use a negative value for the focal length.

Example: if the radius of curvature of a concave lens is 10 cm, the focal length f = -5 cm.

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