Question

The next few questions give you the chance to use the Lens Equation that relates the object distance, Xo, image distance, Xi, and focal length of a lens, F, by: This equation comes from considering the ratio of side lengths of various triangles that are formed in ray diagrams of the type that you have been doing for the last week. There are a few rules you need to follow to play the game and to understand the results. Here is a short list of the most important items 1. For CONVEX lenses, the focal length is POSITIVE. 2. For CONCAVE lenses, the focal length is NEGATIVE. 3. Object distances are always POSITIVE. 4. If you calculate an image distance and the result is positive, then it is on the opposite side of the lens from the object. If instead you find an image distance that is negative, the image is on the same side of the lens as the object. 5. Magnification is the ratio of the height of the image, Si, to the height of the object, So, and is also MINUS the image distance divided by the object distance. So A negative magnification means the image is inverted. A positive magnification means the image is right-side up. Based on the information above, if a CONVEX lens with a focal length of 1.2 cm has an object placed at an object distance of 6.0 cm, what is the image distance? Give your answer in cm to one decimal place of accuracy and remember to include the correct sign. Type your answer...

Answer 1

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1/ x_0 + 1/x_i = 1/ F f = 11.2 cm: X_0 = 6.0cm 1/ x_i = 1/ F - 1/ x_0 = 1/ 1.2 -1/6 = 5 -1/ 6 = 4/6 = 2/ 3 x_i = 1.5 cm M = -x_i/x_0 = -1.5/6.0 = -1/ 4 M = -0.25 f = 2.8cm, x_0 = 2.2 cm 1/ x_i = 1/ 2.8 - 1/ 2.2 = 2.2 - 2.8/ 2.2 times 2.8 = -0.6/ 2.2 times 2.8 x_i = -22 times 2.8/6 = -10.27 cm x_i = -10.27cm M = -(-10.27)/2.2 = 4.67: M = 4.67 f = -3cm, x_0 = 6.6cm 1/x_i = -1/3 - 1/6.6 = -(2.2 + 1)/6.6 = -3.2/6.6 x_i = -2.06cm M = -(-2.06)/ 6.6 = 0.31 m = 0.31