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Phys 155
Lab #5: Lenses and Mirrors
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Why do we see objects?
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The only reason we see anything at all is because light is reflected from objects around us. The reflected light
enters our eyes where it is then focused (our eye is a lens system.)
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Without light, we can’t see. Also, the color of an object depends on the light being reflected from its surface.
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Light is how we detect matter…by seeing it.
Light
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We’ll talk about light in more detail when we study the spectrum but there are a few things that you need to
know for this lab:
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Light is nothing other than a self-sustaining, oscillating combination of electric and magnetic fields
that form a wave. It is this wavelike property that determines light’s behavior when it traverses
through media (lenses, mirrors, etc). We can represent a light wave as a ray that emanates from a
point in all directions.
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Light travels at a constant speed (670,616,629.384 miles/hr) in vacuum. However, when it travels
through a material, it slows down and bends. This effect is called refraction (seen below). Lenses
use refraction to focus light.
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/optpic/brokpen.jpg
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Lenses
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Lenses are devices that bend light in such a way that changes the appearance of an object as seen through
the lens. Usually they are made of glass, but they can be made from just about any transparent material.
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Every lens has a property called the focal length. The focal length determines how “strong” the lens is
and depends on the material and curvature of the lens. Every lens has two focal points: one on
either side of the lens.
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There are two types of lenses:
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Converging Lens (convex or positive): Light that originates from infinity and is parallel to the
optical axis will converge at the lens’ focal point. Converging lenses have positive focal lengths.
Optical Axis
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Suppose we place an object, denoted by a vertical arrow, somewhere near the lens. Light
is reflected off of every single point on the object in all directions, so how do we figure
out what the image will look like? It seems hopeless!
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Even though there are an infinite number of light rays reflected from the object, we can
simplify the problem by considering only two principle rays:
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Ray #1 travels parallel to the optical axis and converges through the focal point
on the other side.
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Ray #2 travels through the vertex (center) of the lens and exits the lens
undeviated.
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So let’s see what happens when the object is placed outside the focal length (fill in
drawing)
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Now let’s move the object so that it lies on the focal point (fill in drawing)
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Now let’s move the object so that it lies closer to the lens than the focal point (fill in
drawing)
SUMMARY:
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When the object distance is larger than the focal length, the image is real and inverted.
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When the object distance is equal to the focal length, the image is inverted and real, but
located at infinity.
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When the object distance is less than the focal length, the image is erect, virtual and
larger than the object.
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What does this mean? As the object is moved closer to the focal point, the image gets
bigger and farther away from the lens until you reach the focal point. At that point, the
image becomes virtual and erect.
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Diverging Lens (or concave or negative): Light that originates from infinity and that is parallel to
the optical axis diverges away from the focal point as it passes through the lens. Diverging lenses
have negative focal lengths.
Let’s draw the same principle rays to see what the image looks like.
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When the object distance is larger than the focal length:
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When the object distance is less than the focal length:
TAKE HOME MESSAGE:
A converging lens produces a virtual image only when the object distance is less than the
focal length. A diverging lens always produces a virtual image!
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Definition of terms:
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Image distance: The distance from the image to the center of the lens.
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Object distance: The distance from the object to the center of the lens.
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Erect: An image is erect if its vertical axis is identical to that of the object.
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Inverted: An image is inverted if the top and bottom are reversed as compared to the object.
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Reverted: An image is reverted if the left and right sides are reversed as compared to the object.
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Real: An image is real if the light rays physically converge at the point where the image is
formed. You can always project a real image onto a screen
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Virtual: An image is virtual if the light rays do not physically converge at the point where the
image is formed, but only appear as though they do; you cannot project the image onto a screen.
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You reflection in a mirror is virtual! Why do you think that is? Does it look like you are
inside the mirror? Can you project your image onto a piece of paper?
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Parallax
We now know that diverging lenses form virtual images that cannot be projected onto screen. So how does one
calculate the image distance for a diverging lens? The answer is that you can make use of a concept called parallax (we
will return to parallax when we study distances to astronomical objects).
Parallax is the apparent shift of an object with respect to the background as the observer moves along a line
perpendicular to the object itself. You can easily observe parallax by holding your right index finger approximately 1 foot
in front of your left index finger. As you move your head from side to side, you’ll notice that one of your fingers moves
right while the other moves left. This intuitive motion is an example of a parallax shift and only occurs when the two
objects (your fingers in this example) are separated by some distance. There is obviously no parallax shift when your
fingers are located in the same place.
So how do we use this concept when finding the location of a virtual image? We first position a reference marker
in between the object and the lens. We then compare the following objects:
#1: The image of the object as seen through the lens
#2: The reference marker as seen outside the lens
As you move your head from side to side, you’ll notice that these two move with respect to each by virtue of the
parallax shift. However, when you move the reference marker either forward or backward, you’ll find a configuration
where the two objects listed above move together as you move your head from side to side. This means that there is no
parallax shift and therefore the reference marker is exactly at the position of the image. The distance from the reference
marker to the lens is subsequently the image distance.
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Lens Maker Formula
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The focal length, object distance, and image distance are related via this simple relation:
1/f = 1/u + 1/v
Where f is the focal length, u is the image distance, and v is the object distance. This is known as the
Lens Maker Formula. It can be used to find any variable if you know the other two. Review adding and
subtracting fractions so that you know how to solve for f, u, or v.
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Mirrors
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As you will see, there are convex and concave mirrors that bend light in much the same way as their lens
counterparts. This is why telescopes can use either lenses or mirrors to focus light.
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Concave mirrors act like convex lenses
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Convex mirrors act like concave lenses