Consider a flat slab made of negative-index material that is placed in air. Assume that a point source is located at the origin of the x-axis, the thickness of the slab is d, and the point source is d/4 away from the first interface of the slab.

(1) If the refractive index n=-1, sketch the light rays to show that two focal points can be formed due to negative refraction. Determine the coordinates of the two focal points by using Snell's law, ray optics and trigonometry.
(2) If the refractive index of the slab is changed to n=-2 while the other conditions are kept the same, can such a slab still form an ideal, point image?

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 740 n/m. it is initially at rest on an inclined plane that is at an angle of theta= 26 with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is uk = 0.17. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. the block's initial mechanical energy is 9.472 j.b. if the spring pushes the block up the incline, what distance l in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.