Calculus Based Physics 3 Question 4

4. Solar sail radiation pressure (30 points) + 5 pts extra credit A solar sail is an idea for a spacecraft that uses a \"sail\" of a highly-reflective maternial 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 generate thrust. The sun's diameter is D..=10 km, and it is located a distance L; ., .=10F km from the lens. The thin converging lens has a diameter De-.=1 km and focal length F The solar sail is circular with diameter O...=1 km and mass m=10 kg. lgnore gravity, oy amil A. (15 points) To reflect the most sunlight, while avoiding overheating from overfocused sunlight, the magnification is chosen such that the image of the sun covers exactly the area of the sail i. At what distance L. i5 the sail placed after the lens to meet this condition? ii. What is the focal length f of the lens? B. (15 points) The solar sail moves with acceleration =107 m/s*. What is the average intensity of light incident on the solar sail? C. {Extra Credit - 5 points) Suppose a filter is used o transmit only 2=500 nm light to the lens. Instead of the condition in part A, now L., is chosen such that the Airy disk exactiy matches the area of the sail (i.e. no diffraction minima appear on the sail). What is the minimum value of L. ..7 Assume L, .= > and =L