lab 5 angular physical sizes continued page 3 0f 6 part the angular and physical diameter of the

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Lab #5: Angular & Physical Sizes (continued) Page 3 of 6 Part 1: The Angular and Physical Diameter of the Sun and Moon You could measure the Sun's angular diameter the same way you did the plate's diameter, but looking at the Sun for even a few moments would do severe damage to your eyes. Instead, you will measure its angular diameter using two approaches: Method 1 requires the direct measurement of the diameter of the Sun's projected image, and Method 2 requires tracking the Sun's apparent motion in the sky. Both methods make use of a pinhole camera. In the diagram below, sunlight enters the pinhole at the end of the tube. Because the Sun has an angular diameter, the light that passes through the pinhole will spread out as it proceeds down the tube. An image of the Sun will appear on the paper placed at the end of the tube. Your instructor will show you a pinhole camera and, if the Sun can be seen through the west-facing windows, may point the camera at the Sun and show you the Sun's actual image. Method 1: Examine the geometry of the light path within the pinhole camera in the diagram below. Note the right triangle that includes half of the Sun's angular diameter. The tangent of this angle can be found if the image width and the tube length are known. 0.5 * Sun's angular diameter pinhole Sun tube length image Tear off the centimeter ruler on page five and use it to measure the width of the Sun's image below. Use a meter stick to measure the tube length in centimeters. Then find the Sun's angular diameter in degrees using the tangent table at the bottom of the page. Repeat the procedure for the Moon's image. A different tube was used to project the Moon image. Sun Moon Sun's image Image width in centimeters Tube length in centimeters Image half-width Tube length tan (0.5) 0.5 Angular diameter (Î¸) Angular diameter (Î¸) 105 cm Moon's image tangent 0.0017 0.0026 0.0035 0.0044 0.0052 0.0061 0.0070 0.0079 0.0087 angle (deg) 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Lab #5: Angular & Physical Sizes (continued)
Page 3 of 6

Part 1: The Angular and Physical Diameter of the Sun and Moon
You could measure the Sun's angular diameter the same way you did the plate's diameter, but looking at the Sun for even a few moments would do severe damage to your eyes. Instead, you will measure its angular diameter using two approaches: Method 1 requires the direct measurement of the diameter of the Sun's projected image, and Method 2 requires tracking the Sun's apparent motion in the sky. Both methods make use of a pinhole camera. In the diagram below, sunlight enters the pinhole at the end of the tube. Because the Sun has an angular diameter, the light that passes through the pinhole will spread out as it proceeds down the tube. An image of the Sun will appear on the paper placed at the end of the tube. Your instructor will show you a pinhole camera and, if the Sun can be seen through the west-facing windows, may point the camera at the Sun and show you the Sun's actual image.

Method 1: Examine the geometry of the light path within the pinhole camera in the diagram below. Note the right triangle that includes half of the Sun's angular diameter. The tangent of this angle can be found if the image width and the tube length are known.

0.5 * Sun's angular diameter
pinhole
Sun
tube length
image

Tear off the centimeter ruler on page five and use it to measure the width of the Sun's image below. Use a meter stick to measure the tube length in centimeters. Then find the Sun's angular diameter in degrees using the tangent table at the bottom of the page. Repeat the procedure for the Moon's image. A different tube was used to project the Moon image.

Sun
Moon
Sun's image
Image width in centimeters Tube length in centimeters Image half-width Tube length tan (0.5) 0.5 Angular diameter (Î¸) Angular diameter (Î¸)
105 cm
Moon's image
tangent 0.0017 0.0026 0.0035 0.0044 0.0052 0.0061 0.0070 0.0079 0.0087 angle (deg) 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

lab 5 angular physical sizes continued page 3 0f 6 part the angular and physical diameter of the sun and moon you could measure the sun angular diameter the same way you did the plate diamet 05593

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