Calculus Based Physics 3 Question 4

4. Solar sall radiation pressure (30 points) + 5 pts extra credit A solar sail la an idea for a spacecraft that uses a 'sall" of a highly-reflective material to reflect sunlight and gain momentum from radiation pressure. Consider the solar sail below. A large lens Images the light from a small sun onto a thin solar sail to generale thrust. The sun's diameter is De 10' km, and it is located a distance from 10* km from the lens The thin converging lens has a diameter Di,"1 km and focal length f. The solar sail is circular with diameter Day =1 km and mass m=10' kg. Ignore gravity. Dam Cosmos-1 solar sail Geometry for problem A. (15 points) To reflect the most sunlight, while avoiding overhealing from ovorfocused sunlight, the magnification is chosen such that the image of the sun covers exactly the area of the sail. i. At what distance Loran is the sail placed after the lens to meet this condition? ii. What is the focal length /of the lens? B. (15 points) The solar sail moves with acceleration a=10* mis'. What Is the average intensity of light incident on the solar sail? C. (Extra Credit - 5 points) Suppose a filter is used to transmit only A=500 nim light to the lens. Instead of the condition in part A, now Lenses is chosen such that the Airy disk exactly matches the area of the sail (i.e. no diffraction minima appear on the sail). What is the minimum value of Les? Assume Larkm 2 and f-Loud