An object is placed 10 m before a convex lens with focal length 4.8 m. Another concave
lens is placed 16.2 m behind the first lens with
a focal length –15 m (see the figure below).
Note: Make a ray diagram sketch in order
to check your numerical answer.
At what distance is the first image from the first lens
Answer in united of m
B. What is the magnification of the first image?
C. At what distance is the second image from the second lens?
Answer in units if m.
D. What is the magnification of the final image, when compared to the initial object ?

Amass m = 74 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius r = 18.4 m and finally a flat straight section at the same height as the center of the loop (18.4 m off the ground). since the mass would not make it around the loop if released from the height of the top of the loop (do you know why? ) it must be released above the top of the loop-the-loop height. (assume the mass never leaves the smooth track at any point on its path.) 1. what is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? 2. what height above the ground must the mass begin to make it around the loop-the-loop? 3. if the mass has just enough speed to make it around the loop without leaving the track, what will its speed be at the bottom of the loop? 4. if the mass has just enough speed to make it around the loop without leaving the track, what is its speed at the final flat level (18.4 m off the ground)? 5. now a spring with spring constant k = 15600 n/m is used on the final flat surface to stop the mass. how far does the spring compress?