Light is incident perpendicularly from air onto a liquid film that is on a glass plate. The liquid film is 70.2 nm thick, and the liquid has index of refraction 1.50. The glass has index of refraction 1.40. Calculate the longest visible wavelength (as measured in air) of the light for which there will be totally constructive interference between the rays reflected from the top and bottom surfaces of the film. Assume that the visible spectrum lies between 400 nm and 700 nm.

After a big snowfall, you take your favorite rocket-powered sled out to a wide field. the field is 195 m across, and you know that your sled accelerates at a rate of 3.65 m/s2 when the rocket is on. how much time will it take the sled to cross the field starting from rest, assuming the rocket is on the whole time?

The inside surface of a cylindrical-shaped cave of inner diameter 1.0 m is continuously covered with a very thin layer of water. the cave is very long and it is open on both ends. the water on the cave surface is at a constant temperature of 15.5 °c. the cave is constantly exposed to wind such that 15.5 °c air flows through the cave at 4.5 m/s. the kinematic viscosity of the air is 14.66 x 10-6 m2/s and the molecular diffusion coefficient of water vapor in the air is 0.239 x 10-4 m2/s. because the cave diameter is so large, the flow of wind down the length of the cave, in the x direction, can be treated like it is external flow and the cave surface can be approximated as flat where appropriate. calculate the x value, in a) the transition to turbulent flow occurs at rex meters, where the air flow transitions from laminar to turbulent along the inside surface of the cave b) calculate the x value, in meters, where the bulk steady state concentration of water vapor in the air flowing in the cave is 10% of the saturation concentration. assume the air at the surface of the water layer is 100% saturated with water vapor. assume the wind entering the cave contained no moisture before it entered the cave. take into account the transition from laminar to turbulent flow when solving part b

Athird point charge q3 is now positioned halfway between q1 and q2. the net force on q2 now has a magnitude of f2,net = 5.861 n and points away from q1 and q3. what is the value (sign and magnitude) of the charge q3?