Final answer:
The type of lens where the single and triple perpendicular lines focus at the same time in lensometry is a converging or convex lens. These lenses converge parallel light rays to a single focal point on the opposite side.
Step-by-step explanation:
The type of lens identified by lensometry when the single and triple perpendicular lines come into focus simultaneously is known as a converging lens or convex lens. This type of lens is characterized by its ability to make parallel light rays that enter it to meet or converge at a single point on the opposite side. This point is known as the focal point of the lens. Converging lenses are thicker at the center than at the edges and have a converging effect on light rays. They are often used to correct farsightedness in eyeglasses or for gathering light in cameras and telescopes. In a practical scenario, when using a converging lens on a sunny day, a bright spot can appear on a paper held beyond the lens, which shows the light rays focusing due to the converging property of the lens.