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Phys4W09HmwkSolutions6

# Phys4W09HmwkSolutions6 - Ray Tracing in Lenses and Mirrors...

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Ray Tracing in Lenses and Mirrors Part A : Which ray is traced through the converging lens correctly? Consider the rays we know to be traced incorrectly. Ray 1 is refracted such that it passes through the focal point. This is true of a ray that it is incident on the lens parallel to the optical axis, which ray 1 is not. Ray 2 is refracted by the lens such that it emerges parallel to the optical axis. This is true for an incident ray that passes through the first focal point, which ray 2 does not. Ray 3 should not be refracted (in the thin lens approximation) as it passes through the center of the lens. Ray 5 passes through the first focal point (not drawn in the problem, but we know that the focal points are the same on both sides of the lens), so it should be drawn such that it is refracted parallel to the optical axis. This leaves only ray 4 that could be traced appropriately. The trace seems reasonable as ray 4 is refracted more than a ray passing through the center of the lens and less than a ray passing through the first focal point, which are the standard rays on either side of ray 4. Part B : Which ray is traced correctly reflecting off of a concave mirror?

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The incident ray is closest to the standard ray that is incident parallel to the optical axis. A ray parallel to the optical axis would be reflected through the focal point, F. The similar rays are rays 2 & 3. Ray 3 is drawn correctly as
Ray Tracing and Image Formation with a Concave Lens Part A : Which diagrams are accurate? The three standard rays drawn to characterize the image in a concave lens are (1) The incident ray parallel to the optical axis that refracts as if the refracted ray originates from F1. (2) The incident ray heading towards F2 that refracts parallel to the optical axis. (3) The ray through the center of the lens that is not refracted. The real diverging rays will never intersect to form an image. To find the image, we project the path of the refracted rays on the object side of the lens to a convergence point. In diagram (A) rays 1 and 3 are traced correctly. (B) ray 1 is traced appropriately. The second ray, heading towards F2, is not refracted in the drawing; it should be refracted parallel to the optical axis. (C) rays 1 and 3 are traced correctly. (D) the ray passing through F2 is not refracted. This is incorrect. The ray passing through F1 emerges parallel to the optical axis, which is incorrect for a diverging lens. So only A and C are correct.

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Part B F = = -7.5 cm, what is d o such that d i =3.7 cm? To determine the object distance, given a focal length and an image distance, we can use the thin lens equation 1/f = 1/d o + 1/d i We can rearrange to solve for the object distance 1/d o =1/f-1/d i =(d i -f)/fd i d o =fd i /(d i -f) We know that the image is always on the object side of a concave lens. By convention, when the image is on the object side of the lens, the object distance is negative.
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