Imagine that once a year in early summer when the black flie

Imagine that once a year, in early summer when the black flies are out in Northern Canada. Santa Claus likes to shave his white beard. On this occasion, he uses a magnifying mirror which was made for him by his elves. They made the mirror by taking the largest spherical reflecting ornament in their shop and cutting it in half. The diameter of the ornament is 30 cm. The mirror which the elves made for Santa is a reflecting hemisphere. If Santa wants to sec a magnified upright image of his face, should he use the inside or outside of the hemisphere? Why\"? Suppose Santa wants the magnified upright image of his chin to be twice as large as his actual chin. Draw a ray diagram which shows where the chin should be placed and how the image is formed. Note: You may want to do part (c) before making your drawing. Exactly where should his chin be located, relative to the mirror, in order to produce a magnified upright image which is twice as large as his actual chin? (Use the mirror equation to find the exact position.) Finally, suppose that Santa gets clever and decides to project an image of a sleigh bell onto a projection screen m such a way that the projected image is three times as large as the actual sleigh bell. Exactly how should he do it? (Make your answer as complete as possible.)

Solution

inside of the hemisphere

If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens converges to a spot (a focus) behind the lens. In this case, the lens is called a positive or converging lens. The distance from the lens to the spot is the focal length of the lens, which is commonly abbreviated f in diagrams and equations.