How do your results from ray tracing compare to your results from using the thin-lens equation? What is the focal length of a convex lens that produces an image 10 cm away with a magnification of -0.5? Show all calculations in your answer.
Hint: Use the definition of magnification and the thin-lens equation.

In the middle of the night you are standing a horizontal distance of 14.0 m from the high fence that surrounds the estate of your rich uncle. the top of the fence is 5.00 m above the ground. you have taped an important message to a rock that you want to throw over the fence. the ground is level, and the width of the fence is small enough to be ignored. you throw the rock from a height of 1.60 m above the ground and at an angle of 54.0 degrees above the horizontal. part a part complete what minimum initial speed must the rock have as it leaves your hand to clear the top of the fence? express your answer with the appropriate units. part b for the initial velocity calculated in the previous part, what horizontal distance beyond the fence will the rock land on the ground?