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.

 f = 6.66 cm

Explanation:

For this exercise we will use the constructor equation

         1 / f = 1 / p + 1 / q

where f is the focal length, p is the distance to the object and q is the distance to the image

the expression for magnification is

          m = h '/ h = - q / p

with this we have a system of two equations with two unknowns, in the problem they give us the distance to the image q = 10 cm and a magnification of m = -0.5

        -0.5 = - q / p

         p = - q / 0.5

         p = - 10 / 0.5

         p = 20 cm

now we can with the other equation look for the focal length

         1 / f = 1/20 + 1/10

         1 / f = 0.15

          f = 6.66 cm

pe = weightxheight = 2000x1000=2,000,000joules

current and voltage can both be different in different parts of a circuit so it matters where you place the ammeter and voltmete