A light ray in air, indicated by the arrow, is incident on a convex glass lens at an angle of 31° to the normal. a) Some of the light will be reflected from the lens. At what angle will it be reflected? b) Find the angle at which the light ray is refracted when entering the lens. (5 points) c) Find the angle at which the ray is incident on the other side of the lens and the angle of refraction when the light ray leaves the lens on that side. For this part, assume the two sides of the lens are sides of an equilateral triangle. Draw the path of the light through the lens and label the angles with their values. (15 points) d) Assume the lens and light source are placed in water (n=1.33). Repeat parts (b) and (c) for this situation. Is the light more, or less refracted? e) Assume now that the initial angle of incidence is changed to 17° while the lens and light source are in air. What happens to the light when it strikes the opposite interface in this case? Calculate the values then state the behavior of the light. f) Find the critical angle for part (e) and for part (e) if the system is placed in water. When analyzing lenses and lens arrangements, it is useful to treat the lenses as “thin” lenses. That is, as if they have no thickness. We can then draw a simple ray-tracing diagram to determine the position and orientation of an image formed by the lens(es) under consideration. g) Consider, again, a convex (converging) lens as above. If an object is 13cm in front of the lens and an image forms 16cm from the lens on the other side, find the focal length of the lens. First, draw and label the raytracing diagram using an upward-pointing arrow as the object. You only need to draw two rays. h) Assume the object is moved to a position of f-2cm, find the new position of the image, its orientation and magnification. Draw the ray-tracing diagram for this situation. i) Consider a concave (diverging) lens. Using the negative of the focal length found in part (g), find the new image position and magnification. Is the image real or virtual? Draw the ray-tracing diagram.
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