Physics

According to Wien's displacement law, as the temperature of a black body increases, the wavelength at which the intensity is maximum shifts towards shorter wavelengths. This means the peak moves to the blue or ultraviolet region as temperature rises.

Potential energy (P.E) in a spring system is proportional to the square of the displacement (x). If P.E is 1/4 of its maximum value, then (x/x')^2 = 1/4, which implies x = x'/2.

The Michelson-Morley experiment was specifically designed to detect the existence of the ether wind, a hypothetical effect caused by the Earth's motion through the luminiferous ether, which was believed to be the medium for light propagation. The experiment used an interferometer to compare the speed of light in perpendicular directions, expecting to observe a difference due to the ether wind. However, the experiment consistently yielded a null result, showing no significant difference in the speed of light in different directions. This null result effectively rejected the existence of the ether wind and the stationary ether concept, leading to the development of special relativity. Other options listed (Young's double-slit experiment, Photoelectric effect, Fizeau's experiment) are unrelated to the detection or rejection of the ether wind.

For a convex lens, the minimum distance between an object and its real image occurs when the object is placed at twice the focal length (2f) from the lens. At this position, the image is also formed at 2f on the other side, making the total distance between object and image 2f + 2f = 4f. However, the question asks for the minimum distance between object and its real image, which is the distance between the two points, i.e., 2f (object at 2f, image at 2f on opposite side, so distance between object and image is 4f). But the standard answer is 4f, so the original correct answer D (4f) is correct. On reconsideration, the minimum distance between object and real image formed by a convex lens is 4f. Therefore, the original correct answer D is correct. The explanation is updated accordingly.

In oscillatory motion, the distance covered in one complete vibration (one full oscillation) is the total path length traveled by the body. The body moves from the mean position to the extreme on one side (amplitude), back through the mean to the extreme on the other side (another amplitude), and then back to the mean position. This total distance is 4 times the amplitude. Given the distance covered in one complete vibration is 20 cm, the amplitude is 20 cm ÷ 4 = 5 cm. Therefore, the correct amplitude is 5 cm, which corresponds to option B.

In a multimode step-index fiber, the core has a higher refractive index than the cladding, which allows total internal reflection to guide light through the fiber. This difference in refractive indices is essential for the fiber's operation.

The point where incident parallel rays of light converge or appear to diverge after passing through a lens is called the focus. This is a fundamental concept in optics related to how lenses form images.

Resonance is a phenomenon where a system oscillates with greater amplitude at specific frequencies. Devices like TVs, radios, and microwave ovens operate based on resonance principles (e.g., tuning circuits or microwave cavity resonance). A bulb, however, works by electrical resistance heating and does not rely on resonance.

The length of a seconds pendulum is defined as the length of a pendulum that has a period of exactly 2 seconds (1 second for a half swing). This length is approximately 100 cm (1 meter) on Earth at standard gravity. Therefore, option A (100 cm) is correct.

The power of a lens is measured in diopters, which is the reciprocal of the focal length in meters. This unit quantifies the converging or diverging ability of the lens.