The dispersion characteristics of the left-handed material prism and the equal-inclination interference characteristics of parallel plate of the left-handed material are studied. For prism of the left-handed material, the deflecting direction of the exit light deviating from the original propagation direction is contrary to that of prism of the right-handed material. The deviation angle of prism of the left-handed material is larger than that of prism of the right-handed material for the same monochromatic light with equal incident angles. The formulas of intensity distribution of the reflected light and transmitted light at the focal planes are derived for investigating the characteristics of parallel plate the left-handed material. The relation between bright and dark fringes of equal-inclination interference and their orders is analyzed. The formulas of bright rings′ radii and dark rings′ widths in the case of half-wave loss are derived. For the equal-inclination interference characteristics of parallel plate of the left-handed material, the orders of fringes of equal-inclination interference are lower at the center of circular rings, which is different from the case of parallel plate of the right-handed material.