Statement I : The mirror used in searchlight is parabolic. Statement I : All the rays coming from the source at the focus of a parabolic mirror are reflected as an intense parallel begun.

Statement I is true as searchlights utilize parabolic mirrors to project light over long distances. Statement II is also true and provides the correct scientific explanation for Statement I. According to the geometric properties of a parabola, any light source placed at its focal point emits rays that, upon reflection, emerge as a perfectly collimated or parallel beam. While spherical mirrors suffer from spherical aberration where parallel rays do not meet at a single point, parabolic reflectors eliminate this issue, ensuring that all light from the focus is directed into an intense, narrow, and parallel beam [1]. This property makes them ideal for searchlights, car headlights, and flashlights where a concentrated beam is required. Thus, Statement II correctly explains why the parabolic shape is chosen for searchlights.

Sources

1. [1] https://en.wikipedia.org/wiki/Parabolic_reflector