Physics

A convex lens produces a virtual image only when the object is placed between the principal focus (F) and the optical center (O) of the lens. In this position, the rays diverge after refraction, and the image formed is virtual, erect, and magnified.

The frequency of a second pendulum is defined as one oscillation per two seconds, which corresponds to 0.5 hertz (since frequency is the reciprocal of the period).

A scanning electron microscope (SEM) produces detailed three-dimensional images of a sample's surface by scanning it with a focused beam of electrons, unlike a standard electron microscope which typically provides two-dimensional images.

The dioptre power (P) of a lens is given by the formula P = 100 / focal length (in cm) or equivalently P = 1 / focal length (in meters). For a concave lens, the focal length is negative. Given the focal length is 10 cm, the focal length in meters is 0.10 m, so the power is P = 1 / (-0.10) = -10 dioptres. Therefore, the correct answer is -10 dioptres, which corresponds to option A.

The Davisson-Germer experiment demonstrated the wave nature of electrons (not protons) by showing electron diffraction patterns when electrons were scattered off a crystal. This confirmed the wave property of matter as predicted by de Broglie.

The natural frequency of a simple pendulum depends on the length of the pendulum and the acceleration due to gravity. Specifically, the frequency is inversely proportional to the square root of the length, not directly the square root of the length itself. Therefore, the correct answer is that it depends on its length.

The sharpness of resonance, often quantified by the quality factor (Q), is inversely proportional to the damping force. Higher damping reduces the sharpness of resonance, making the system less selective in frequency response.

The uncertainty in momentum and position arises from the fundamental property of matter and radiation described by quantum mechanics, specifically the Heisenberg Uncertainty Principle. This principle states that certain pairs of physical properties cannot both be known to arbitrary precision simultaneously.

The stopping potential depends on the maximum kinetic energy of emitted electrons, which is determined by the frequency of the incident light and the work function of the metal. It does not depend on the intensity or threshold frequency alone.

According to special relativity, as an object with mass approaches the speed of light, its relativistic mass increases without bound, effectively becoming infinite at the speed of light. This makes it impossible for material objects with mass to reach the speed of light.