This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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The image you provided outlines objectives for reflection of light at plane and curved surfaces, not refraction. I will generate notes based on the objectives for reflection as stated in the image. Here are notes for the UTME exam on Reflection of Light at Plane and Curved Surfaces: i. Laws of Reflection: The incident ray, the reflected ray, and the normal* to the surface at the point of incidence all lie in the same plane. The angle of incidence (_i) is equal to the angle of reflection* (_r). That is, _i = _r. ii. Image Formation by Mirrors: Plane Mirror: Forms a virtual, erect, and laterally inverted* image that is the same size as the object and located as far behind the mirror as the object is in front. Concave Mirror: Can form both real and virtual images, depending on the object's position. Real images are inverted, while virtual images are erect and magnified*. Convex Mirror: Always forms a virtual, erect, and diminished* image, located behind the mirror between the pole and the principal focus. iii. Mirror Formula: The relationship between object distance (u), image distance (v), and focal length (f) for spherical mirrors is given by: (1)/(f) = (1)/(u) + (1)/(v) Sign Conventions (Cartesian): Distances measured in the direction of incident light are positive; opposite are negative. Distances above the principal axis are positive; below are negative. For concave mirrors, f is positive. For convex mirrors, f is negative. Real objects and real images have positive u and v respectively. Virtual images have negative v. iv. Linear Magnification: Linear magnification (M) is the ratio of the height of the image (h_i) to the height of the object (h_o), and also the ratio of the image distance (v) to the object distance (u): M = (h_i)/(h_o) = -(v)/(u) If M > 1, the image is magnified. If M < 1, the image is diminished. If M = 1, the image is the same size. If M is positive, the image is erect (virtual). If M is negative, the image is inverted (real). v. Applications of Reflection: Periscope: Uses two plane mirrors (or prisms) arranged parallel to each other at a 45-degree angle to allow viewing over, around, or through an obstacle. Light reflects off the first mirror, then off the second, to the observer's eye. Kaleidoscope: Consists of multiple mirrors (usually three) arranged at an angle to each other, creating multiple reflections of objects (often colored beads or pieces of glass) to form symmetrical patterns. Sextant: An instrument used to measure the angle between two objects, typically the horizon and a celestial body (like the sun or a star), for navigation. It uses mirrors to bring the image of the celestial body into coincidence with the horizon.