It has been proposed that a spaceship might be propelled in the solar system by radiation pressure, using a large sail made of foil. How large must the surface area of the sail be if the radiation force is to be equal in magnitude to the Sun’s gravitational attraction? Assume that the mass of the ship + sail is 1500 kg, that the sail is perfectly reflecting, and that the sail is oriented perpendicular to the Sun’s rays. See Appendix C for needed data. (With a larger sail, the ship is continuously driven away from the Sun.)
The surface area of the sail, .
Mass of ship and sail, m=1500kg .
Sail is perfectly reflected.
Here, we need to use the concept of force developed due to the radiation pressure. The force acting on a perfectly reflective surface of the area as a result of incident radiation of intensity I is given by , where is the speed of light.
Formulae are as follows:
For purely reflecting surface, the radiation pressure, .
Where c is the speed of light, and I is the intensity of radiation.
Attractive force due to Sun on mass m is,
Where MS is the mass of the sun, F is the force, d is the distance.
The spaceship is propelled in the solar system by the radiation pressure, and at the same time, it’s attracted by the sun. So write force equations as follows:
Where A is the surface area of the sail, and p is the radiation pressure, and where Fs, Fr are forces due to sun and radiation.
For purely reflecting surface, radiation pressure,
Hence, the Surface area can be calculated as,
Substitute the values in the above expression, and we get,
Therefore, the surface area of the sail, 9.5x105 m2 .
Question: In Fig. 33-62, a light ray in air is incident at angle on a block of transparent plastic with an index of refraction of . The dimensions indicated are and . The light passes through the block to one of its sides and there undergoes reflection (inside the block) and possibly refraction (out into the air). This is the point of first reflection. The reflected light then passes through the block to another of its sides — a point of second reflection. If , on which side is the point of (a) first reflection and (b) second reflection? If there is refraction at the point of (c) first reflection, and (d) second reflection, give the angle of refraction; if not, answer “none”. If , on which side is the point of (e) first reflection and (f) second reflection? If there is refraction at the point of (g) first reflection, and (h) second reflection, give the angle of refraction; if not, answer “none”.
(a) Prove that a ray of light incident on the surface of a sheet of plate glass of thickness emerges from the opposite face parallel to its initial direction but displaced sideways, as in Fig. 33-69. (b) Show that, for small angles of incidence , this displacement is given by
where is the index of refraction of the glass and is measured in radians.
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