Chapter 1, Problem 21RCQ

Poke a hole in a piece of cardboard and hold the cardboard horizontally in the sunlight (as in Figure 1.6). Note the image of the Sun that is cast below. To convince yourself that the round spot of light is an image of the round Sun, try using holes of different shapes. A square or triangular hole will still cast a round image when the distance to the image is large compared with the size of the hole. When the Sun's rays and the image surface are perpendicular, the image is a circle; when the Sun's rays make an angle with the image surface, the image is a "stretched-out" circle, an ellipse. Let the solar image fall upon a coin, say a dime. Position the cardboard so the image just covers the coin. This is a convenient way to measure the diameter of the image-the same as the diameter of the easy-to-measure coin. Then measure the distance between the cardboard and the coin. Your ratio of image size to image distance should be about . $\frac{1}{110}$ This is also the ratio of the Sun's diameter to its distance to Earth. Using the information that the Sun is 150,000,000 kilometers from Earth, calculate the diameter of the Sun. (Interesting questions: How many coins placed end to end would fit between the solar image and the cardboard? HOW many suns would fit between the card and the Sun?)