In the diagrams below, we show these points from the above figure rotated so that the surface of the lens is horizontal. This second orientation is useful to compare the incident rays of light as they come upon the air-lens interface.
In each case, draw the normal to the surface of the lens on the diagrams that are boxed on the right, and label the incident angles for each ray and heta _(B), respectively). Which ray will refract more after passing into the lens? Explain using Snell's law.
Ray Tracing
Most lenses are constructed so that one or both sides of the lens are spherical in shape. That is, each side of the lens forms a small portion of a large sphere. By doing so, rays of light that are parallel as they enter the lens will converge to a single point known as the focal point. ^(1) In practice, we define two focal points: one to the left and one to the right of the lens, both a distance f (the focal length) from the center of the lens.
If we place an object to the left of the lens, we can use these focal points to construct an image formed by our lens through a technique known as ray tracing. This technique can be derived rigorously, however we will just consider simple rules we can use to find the image. We will denote our object as a vertical arrow as shown below, where the tail of the arrow lies on the principal axis, the horizontal line drawn through the center of the lens. To find the image formed by the lens, we consider three principal rays (shown in the image below):
Ray 1 is parallel to the principal axis and is refracted such that it passes through the focal point on the right side of the lens.
Ray 2 passes through the focal point on the left of the lens and refracts such that it emerges from the lens parallel to the principal axis.
Ray 3 passes through the center of the lens is is not refracted at all.
The image is formed by drawing our arrow from the principal axis to the point where these three rays meet. If this method is done carefully with rulers and proper scaling (that is, all distances in the figure are to scale), this can be a useful quantitative method to determine the location and properties of the image. We will primarily use this as a qualitative method, and often only two of the three principal rays are needed for this (using three rays guarantees that you are drawing them correctly).
'In actuality, the rays never converge precisely to a single point, due to an effect known as spherical aberration, but we will not worry about this for the purposes of today's lab.
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air-lens interface.
1. In each case,draw the normal to the surface of the lens on the diagrams that are boxed on the right, and label the incident angles for each ray A and , respec- tively. Which ray will refract more after passing into the lens? Explain using Snell's law.
Point A
Point B
Ray Tracing Most lenses are constructed so that one or both sides of the lens are spherical in shape. That is,each side of the lens forms a small portion of a large sphere. By doing so,rays of light that are parallel as they enter the lens will converge to a single point known as the focal point. In practice, we define two focal points: one to the left and one to the right of the lens, both a distance f (the focal length from the center of the lens. If we place an object to the left of the lens, we can use these focal points to construct an image formed by our lens through a technique known as ray tracing. This technique can be derived rigorously, however we will just consider simple rules we can use to find the image. We will denote our object as a vertical arrow as shown below, where the tail of the arrow lies on the principal axis, the horizontal line drawn through the center of the lens. To find the image formed by the lens, we consider three principal rays (shown in the image below): Ray 1 is parallel to the principal axis and is refracted such that it passes through the focal point on the right side of the lens. Ray 2 passes through the focal point on the left of the lens and refracts such that it emerges from the lens parallel to the principal axis Ray 3 passes through the center of the lens is is not refracted at all.
not worry about this for the purposes of today's lab.
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