Huygen's Wave Theory and Wave Optics

The Huygen's construction of wavefront does not explain the phenomena of spectra.

Wavefront is the locus of all points, where the particles of the medium vibrate with the same phase.

According to the Huygens theory, all the points on a  wavefront act as source for a secondary wavefront or a wavelet which spread outward from the point and move at the speed of light.

The Huygen's construction of wavefront does not explain the phenomena of origin of spectra.

Wavefront is the locus of all points, where the particles of the medium vibrate with the same phase

When a wave reflects from a rarer medium, there is no phase change. Therefore, the crest remains a crest and the trough remains a trough.

As the waves propagates, it goes on creating secondary sources of light, resulting in increase in its radius.

Huygens's Principle states that every point on a wavefront is a source of secondary wavelets, which spread forward at the same speed.

• when you considered it a large distance and measuring justice Mall section of it then it can be considered to be plane wavefront source at Infinity 
• example the one coming from sun to earth surface is considered to be plain VU friend from light diverging from a point source will be spherical
• So, the wave front due to a source situated at infinity is planar
• Option  C is the right answer

• Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves  also experience refraction. 
• How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.
• Hence refraction is used to analyse a beam of light into its component wavelength
• Option B is the right answer

Ray optics is valid when characteristics dimensions are larger than the wavelength of the light, so that rectilinear property of light can be used.

Huygens 

A wave front is the locus of points having the same phase.
Thus statement A is true because the phase difference is zero as all points have same phase.
Statement R is true because a wavefront is composed of all points where the light reaches from the source in the same time.
As light takes the same time it has the same phase at all points on a wavefront and hence it correctly explains statement A.

Primary wave can travel in all directions in ether.
Secondary waves can travel in forward direction in ether

Huygen considered, light needs a medium to propagate  called ether which is highly elastic and less denser.

B

Wave front formed by the collimator of a spectrometer is a plane wave front, when r lit is in the focus.

Huygen's wave theory: This wave theory was given by Huygens in 1678. According to this theory, a source of light propagates spherical waves in hypothetical.

Huygen proposed a hypothesis for the geometrical construction of the position of a common wavefront at any instant during the propagations of waves in a medium.

Given,

Maximum intensity I_max is proportional to (a1 + a2)^2 = 100 units, meaning a1 + a2 = 10. Reducing the width of one source by 50% reduces its amplitude by a factor of sqrt(0.5). Solving for the new amplitudes and calculating the new maximum intensity via (a1 + a_new)^2 yields approximately 72.85 units.

At the first minimum, the path difference between the edges of the slit is lambda. The path difference between the edge and the midpoint is lambda/2, which corresponds to a phase difference of pi.

In ordinary light sources, light is emitted due to independent atomic transitions lasting roughly 10^-8 seconds, during which the phase remains relatively constant before a sudden random phase change occurs.

Huygens' theory proposed that light propagates as a wave through a hypothetical medium called the luminiferous ether.

In a parallel beam of light (plane wave), the energy density remains constant as it propagates, assuming no absorption or scattering.

Huygens principle states that every point on a wavefront acts as a source of secondary spherical wavelets, allowing us to geometrically construct the position of a wavefront at any subsequent time.

Coherent sources can be created by dividing the wavefront (e.g., Young's double slit) or by dividing the amplitude (e.g., thin film interference).

Christian Huygens postulated wave theory.

Reflected wave is inverted hence second medium is dir sec with respect to first medium. $\lambda ' < \lambda $

A wavefront originating from a localized point source spreads out uniformly in all directions in three-dimensional space, forming expanding concentric spheres at finite distances.

Polarization is a phenomenon that only occurs with transverse waves, as it requires the oscillation to be perpendicular to the direction of propagation.

Since the refractive index increases with height, the upper part of the light beam travels slower than the lower part near the ground. According to Huygens' principle, this differential speed causes the wavefronts to tilt such that the beam bends upward.

On reflection from denser medium, phase reversal occurs i.e. phase change $=\pi$ takes place, because glass is much denser than water.

On reflection from a plane surface velocity and amplitude of the incident ray changes whereas wavelength and frequency does not change.

The above statement is true.

Newton has given the theory that light is made of tiny particles. In 1678, Dutch physicist, Christiaan Huygens, believed that light was made up of waves vibrating up and down perpendicular to the direction of light, and therefore formulated a way of visualizing wave propagation. This known as 'Huygens' Principle'. 

Huygens believed that light was made up of waves vibrating up and down perpendicular to the direction of  the light travels. This is known as 'Huygens' Principle'.  According to this theory, light waves are spherical, and these wave surfaces advance or spread out as they travel at the speed of light. This theory explains why light shining through a pin hole or slit will spread out rather than going in a straight line.

In interference patterns from two point sources, the locus of points with a constant path difference (and thus constant phase difference) is a hyperbola.

According to convention, direction of wave propagation is along the normal to wavefront.

Corpuscular theory fails to explain the velocity of light in air and water because it predicted light to have more velocity in denser medium where as the fact is just the opposite. So option (a) is correct.

$Answer:$ B

All particles in it have same phase.

A wave front is the locus of points having the same phase.
Hence option A is correct.

Due to the large distance, the radius of the wavefront can be considered as large (infinity) and hence, a wavefront is almost plane.

The wave front equations must be of form $ax+by+cz=1$ where ${a^2} + {b^2} + {c^2} = 1$ 

Given the direction of propagation is $ \hat{i} $
Wave fronts will be planes $ \perp \hat{i} $
In the given options, only plane $ x=c $ is  $ \perp \hat{i} $

A wavefront is the locus of points characterized by propagation of position of the same phase: a propagation of a line in 1D, a curve in 2D or a surface for a wave in 3D.

 A wavefront is the locus of points having the same phase.