Wave Optics

10.4 Distance between the slits, d = 0.28 mm = 0.28 $*{10}^{-3}$ m

Distance between the slits and the screen, D = 1.4 m

Distance between the central bright fringe and the fourth ( n = 4) fringe, u = 1.2 cm = 1.2 $*{10}^{-2}$ m

In case of a constructive interference, we have the relation for the distance between two fringes as : u = n $?\frac{D}{d},$ where n = order of fringes = 4 and $?$ = wavelength of the light used

Hence,  $?$ = $\frac{ud}{nD}$ = $\frac{1.2\mathrm{}*{10}^{-2}*0.28\mathrm{}*{10}^{-3}}{4*1.4}$ = 6 $*{10}^{-7}$ m = 600 $*{10}^{-9}$ m = 600 nm

Hence, wavelength of the light is 600 nm.

10.3 The refractive index of glass,  $?$ = 1.5

Speed of light in vacuum, c = 3.0 $*{10}^8$ m/s

Speed of light in glass is given by the relation,  $v$ = $\frac{c}{?}$ = $\frac{3.0\mathrm{}*{10}^8}{1.5}$ = 2 $*{10}^8$ m/s

The speed of light in glass is not independent of the colours of light. The refractive index of a violet component of white light is less than the speed of red light in glass. Hence, violet light travels slower than red light in a glass prism.

Ans.10.2 The shape of the wave front in case of a light diverging from a point source is spherical.

The shape of the wave front in case of a light emerging out of a convex lens when a point source is placed at its focus is a parallel grid.

The portion of the wave front of light from a distant star intercepted by the Earth is a plane.

Diffraction leads to the formation of patterns of varying intensity. When around obstacles, waves bend and spread through the narrow opening, it is called diffraction. The interference results in a new wave pattern and involves the superposition of two or more coherent waves. Both these phenomena produce patterns of light and dark regions; the interference results from the combination of multiple waves and the diffraction arises from a single wave interacting with an aperture or obstacle. When the size of the aperture or obstacle is comparable to the wavelength of the wave, diffraction patterns are typically observed.

A coherent light source in Young's Double Slit Experiment illuminates two closely spaced slits, and produces two overlapping light waves. The interference of these waves constructively or destructively based on their phase difference lead to a pattern of bright and dark fringes on a screen, When the path difference is an integral multiple of the wavelength, it is constructive interference (bright fringes) and when the path difference is an odd multiple of half the wavelength, it is destructive interference (dark fringes). Through observable interference patterns, Young's Double Slit Experiment, shows the wave nature of light.

The Davisson-Germer experiment was conducted to test the De-broglie hypothesis and know wave nature of electrons. In this experiment, a beam of electrons was emitted from an electron gun with known acceleration to strike a nickel crystal placed inside a vacuum chamber.

After striking the surface, electrons are scattered from the crystal surface at different angles. The diffraction pattern obtained through this experiment was similar to that produced by X-rays, which is wave.

The Davisson-Germer experiment provided the first experimental proof of the wave nature of matter and de Broglie's hypothesis right.

Significance of de Broglie's Hypothesis in Modern Physics (NCERT-based answer):

De Broglie's hypothesis is a revolutionary idea which changed the understanding of matter and wave as we know it. This hypothesis introduced the concept that particles of matter, like electrons, and Proton, can behave like wave and have wave-like properties, just as light exhibits both wave and particle nature.

According to de Broglie, any moving particle has a wavelength given by:

$\lambda = \frac {h} {p} = \frac {h} {mv}$

where $\lambda$ is the wavelength, $h$ is Planck's constant, $m$ is the mass, and $v$ is the velocity of the particle.

The photoelectric effect when light is projected in a metal surface, it's surface ejects electron (which are in outermost shell or free electron). This happens because the light provides additional energy to the electron to detach itself from metal surface. Well to do this light must have a certain amount of energy which in other words can be said the right frequency of light is required for photoelectric effect. 

This frequency must be above a certain minimum value (called threshold frequency) fixed for every metal, regardless of its intensity. Photoelectric effect cannot be explained by the wave theory of light.