🔑:## Step 1: Understanding the ScenarioThe observer is moving at a significant fraction of the speed of light towards a clock tower. According to special relativity, as the observer approaches the clock tower, time dilation occurs, causing time to appear to pass more slowly for the observer relative to a stationary observer at the clock tower.## Step 2: Applying Time DilationFrom the perspective of the moving observer, time dilation causes the clock on the approaching tower to appear to run slower compared to the observer's own clock. This means that as the observer gets closer to the clock tower, the hands of the clock on the tower will appear to move more slowly.## Step 3: Considering the Doppler EffectThe Doppler effect also plays a role in this scenario. As the observer approaches the clock tower, the frequency of the light emitted by the clock (or any signal from it) increases due to the Doppler shift. This means that the observer will perceive the clock's signals (such as the ticking or the movement of the hands) as happening more frequently.## Step 4: Combining Time Dilation and Doppler EffectHowever, the Doppler effect does not directly counteract the time dilation effect on the perceived movement of the clock hands. The time dilation effect makes the clock appear to run slower, while the Doppler effect would make the signals from the clock appear more frequent. But in terms of visual observation of the clock hands moving, the dominant effect is time dilation, making the clock hands appear to move slower.## Step 5: Limiting Case - Approaching the Speed of LightAs the observer's speed approaches the speed of light, the time dilation effect becomes more pronounced. The clock on the approaching tower will appear to almost stand still, with the hands moving extremely slowly from the observer's perspective. The Doppler effect, in the limit, would make the light from the clock appear more and more blue-shifted, but the visual perception of the clock's hands would be dominated by the extreme time dilation.The final answer is: boxed{0}

🔑:## Step 1: Understanding the Basics of Photon-Atom CollisionsWhen a photon collides with an atom, it can either be absorbed, scattered (elastically or inelastically), or the atom can remain unaffected if the photon's energy does not match any of the atom's energy transitions. The collision is considered elastic if the photon's energy (and thus its frequency) remains unchanged after the interaction, and inelastic if the photon's energy changes.## Step 2: Elastic ScatteringElastic scattering occurs when the photon's energy is not sufficient to excite the atom to a higher energy state, but is rather scattered in a different direction without any energy transfer. This process is also known as Rayleigh scattering and is responsible for the blue color of the sky, as shorter (blue) wavelengths are scattered more than longer (red) wavelengths by the atmosphere.## Step 3: Inelastic ScatteringInelastic scattering happens when the photon's energy is absorbed by the atom, exciting an electron to a higher energy level. If the photon's energy matches exactly the energy difference between two levels, the process is said to be resonant. After absorption, the excited electron can decay back to its original state, emitting a photon. This process is known as fluorescence if the emitted photon has less energy than the absorbed one (due to non-radiative losses) or as resonance fluorescence if the emitted photon has the same energy as the absorbed one.## Step 4: Role of ResonanceResonance plays a crucial role in determining the likelihood of absorption. When the photon's energy matches the energy difference between two atomic levels, the probability of absorption increases significantly. This is because the atom is more likely to interact with the photon when its energy corresponds to a natural frequency of the atom.## Step 5: Decay Channels of the Excited ElectronAfter an electron is excited by a photon, it can decay through various channels. The primary radiative decay channel is the emission of a photon as the electron falls back to a lower energy level. Non-radiative decay channels include collisions with other electrons or nuclei, leading to the conversion of excess energy into heat or other forms of energy. The specific decay channels available depend on the atom's energy level structure and the environment (e.g., presence of other atoms or molecules).## Step 6: Emission of Another Photon Immediately After AbsorptionIf another photon is emitted immediately after absorption, the process can still be considered inelastic if the emitted photon has a different energy than the absorbed one. However, if the emitted photon has the same energy as the absorbed one and the process occurs without any significant delay (on the timescale of atomic transitions), it can be classified as elastic scattering, specifically as resonance fluorescence. This is because, from an energy perspective, the photon is scattered without any net energy transfer to the atom.The final answer is: boxed{Elastic}

🔑:## Step 1: Understanding the SetupThe problem describes a U-shaped conductor placed between two parallel plates of a capacitor, with the bottom of the U perpendicular to the centers of the plates and the legs of the U adjacent and parallel to the inner surfaces of the plates. The capacitor is connected to a DC voltage source.## Step 2: Electrostatic InductionWhen the capacitor is connected to a DC voltage source, an electric field is generated between the plates of the capacitor. This electric field induces charges on the surfaces of the U-shaped conductor due to electrostatic induction. The charges induced on the conductor are such that they oppose the external electric field.## Step 3: Charge Distribution on the ConductorGiven the geometry, the electric field lines between the capacitor plates are parallel to the legs of the U. The charges induced on the U-shaped conductor will distribute in such a way that they cancel out the electric field within the conductor. Since the legs of the U are parallel to the electric field lines, there is no electric field component perpendicular to the legs that would cause a voltage difference along the length of the legs.## Step 4: Voltage Measurement Across the LegsSince there is no electric field within the conductor (due to the induced charges canceling out the external field) and the electric field outside is parallel to the legs of the U, there is no potential difference (voltage) between points along the length of the legs. This means that if you were to measure the voltage across the legs of the U, you would measure no voltage.## Step 5: Role of Electrostatic InductionElectrostatic induction plays a crucial role in this scenario. It is the process by which the external electric field induces charges on the conductor, which in turn affects the distribution of charges within the conductor. This induction ensures that the electric field within the conductor is zero, which is a fundamental property of conductors in electrostatic equilibrium. The induced charges on the U-shaped conductor are responsible for the absence of a measurable voltage across its legs.The final answer is: boxed{0}

🔑:## Step 1: Understand the initial setupThe point source of light (S) is placed a distance (d) in front of the screen (A), and the intensity of the light at the screen is given as 1 intensity unit.## Step 2: Consider the effect of introducing the mirrorWhen the completely reflecting mirror (M) is placed a distance (d) behind the source, it reflects the light back towards the screen. This reflected light will also reach the screen, contributing to the total intensity.## Step 3: Calculate the intensity of the reflected lightSince the mirror is completely reflecting and is placed at the same distance (d) behind the source as the source is in front of the screen, the path length for the reflected light to reach the screen is twice the distance (2d). However, the intensity of light decreases with the square of the distance due to the inverse square law. Thus, the intensity of the reflected light at the screen will be (1/(2d)^2) = 1/4 of the intensity of the primary source at the same distance d.## Step 4: Calculate the total intensity at the screenThe total intensity at the screen will be the sum of the intensity of the primary source and the intensity of the reflected light. Given that the primary source's intensity at the screen is 1 unit, and considering the mirror's reflection, the total intensity (I_total) can be calculated as I_total = 1 (primary intensity) + 1/4 (reflected intensity).## Step 5: Calculate the final intensityI_total = 1 + 1/4 = 5/4.The final answer is: boxed{1.25}