This question tests knowledge of image formation by a concave mirror, specifically when the object is placed at the center of curvature. We need to recall the rules of ray tracing or the mirror formula to determine the nature, position, and size of the image.
Therefore, an object placed at the center of curvature of a concave mirror forms a real, inverted, and same-sized image at the center of curvature.
Correct Option: C) Real, inverted, and of the same size as the object
The question asks why convex mirrors are preferred as rear-view mirrors in vehicles. We need to analyze the properties of convex, plane, and concave mirrors, especially concerning image formation and field of view, to determine the most suitable type for this application.
Correct Option: D) A convex mirror provides a wider field of view (covers a larger area behind the vehicle) and always forms a diminished, erect image
The question asks about spherical aberration in concave mirrors and how aperture size affects image sharpness for a given focal length. Spherical aberration occurs because parallel rays far from the principal axis do not converge at the same focal point as rays close to the axis. We need to determine how to minimize this effect to produce a sharper image.
C) A concave mirror with a smaller aperture (opening). A smaller aperture restricts the incident light to paraxial rays, which converge more accurately at the focal point, thereby minimizing spherical aberration and producing a sharper image.
The question asks for the definition of refraction of light. We need to evaluate each option based on the fundamental principles of light phenomena.
D) Changes direction (bends) as it passes from one transparent medium into another, due to a change in its speed
This option correctly defines refraction. When light travels from one medium to another (e.g., from air to water), its speed changes. This change in speed causes the light ray to bend or change direction, a phenomenon known as refraction. The extent of bending depends on the refractive indices of the two media and the angle of incidence, as described by Snell's Law:
\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]where \(n_1\) and \(n_2\) are the refractive indices of the first and second media, respectively, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction.
Refraction is a fundamental phenomenon in optics where light bends as it passes from one medium to another. Understanding its physical mechanism requires considering how light interacts with different materials.
C) The change in the speed of light as it passes from one medium to another. This is the direct physical cause of the bending of light during refraction. When light enters a denser medium, it slows down, and if it enters at an angle, this change in speed causes it to bend towards the normal. Conversely, when it enters a less dense medium, it speeds up and bends away from the normal.
The question asks for the mathematical expression of Snell's Law of refraction. Snell's Law describes the relationship between the angles of incidence and refraction, and the refractive indices of the two media involved when light passes from one medium to another.
This equation shows that the product of the refractive index of a medium and the sine of the angle of the light ray in that medium (with respect to the normal) is constant across the interface between two media.
A) \(n_1 \sin \theta_1 = n_2 \sin \theta_2\) is the correct mathematical expression for Snell's Law of refraction. It accurately describes the relationship between the refractive indices and the angles of incidence and refraction.