When a wave enters a new medium, slows down, and bends, the wave undergoes a) reflection b) absorption c) refraction d) reduction

What happens to the light rays when they hit the specimen?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.

When the displacement of a mass on a spring is 12a the half of the amplitude, what fraction of the mechanical energy is kinetic energy? at what displacement, as a fraction of a, is the mechanical energy half kinetic and half potential?