Physics

Single mode step index fibers minimize transmission errors because they allow light to travel a single path, reducing modal dispersion and signal distortion. Graded index fibers reduce modal dispersion compared to multimode step index fibers but are less effective than single mode fibers in minimizing errors.

The equation θ = 1.22 λ/D describes the angular resolution limit due to diffraction for a circular aperture and is known as the Rayleigh criterion, named after Lord Rayleigh who formulated it.

A second pendulum is defined as a pendulum with a time period of exactly 2 seconds, meaning it takes 1 second to swing in one direction and 1 second to return, totaling 2 seconds per full oscillation.

In modern optical fiber communication systems, repeaters or optical amplifiers are typically placed every 20 km to maintain signal strength and quality over long distances. Distances like 100 km or more are generally too long without amplification in newer systems.

A collimator in a spectrometer produces parallel beams of light, which is essential for accurate measurement and analysis of spectra. This ensures that the light entering the spectrometer is well-directed and uniform.

Spherical aberration occurs when light rays passing through a lens near its edge fail to converge at the same point as rays passing near the center, causing a blurred image. This is common in lenses with large apertures. Chromatic aberration, on the other hand, is due to different wavelengths focusing at different points.

The magnification of an astronomical telescope is given by the ratio of the focal length of the objective lens (fo) to the focal length of the eyepiece (fe), i.e., magnification = fo/fe. This is because the telescope enlarges the angular size of the object by this ratio, making the image appear larger to the observer.

In optical fiber transmission systems, repeaters are used to regenerate the dim light signals by amplifying and reshaping them, ensuring the signal can travel long distances without significant loss.

The rate of emission of photons is given by the power divided by the energy per photon. Since the energy per photon is E = hc/λ, the rate of emission = P / (hc/λ) = Pλ / (hc). Thus, the rate depends on the wavelength λ, Planck's constant h, speed of light c, and power P, not just a single constant or speed.

The Stefan-Boltzmann law (also called Stefan's law) states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature (in Kelvin). This is mathematically expressed as M = σ T^4, where σ is the Stefan-Boltzmann constant. The law is named after Josef Stefan and Ludwig Boltzmann. Planck's law describes the spectral distribution of blackbody radiation but does not express the total energy proportionality to T^4. Wien's law relates to the wavelength at which the emission is maximum, and Rayleigh-Jeans law is an approximation valid at long wavelengths. Therefore, the correct answer is Stefan's law (option C).