Antinodal curves correspond to constructive interference.
When light is passed through a double slit opening, light from the two slits interfere at different points in the screen, forming alternating bright and dark fringes due to constructive and destructive interference respectively. However the intensities of higher order bands is slightly diminished.
Such an arrangement was first studied by Young, and has been since called Young's Double Slit Setup.
Reflection, interference and diffraction are the phenomena shown by both transverse waves and longitudinal waves. Polarization is the phenomenon shown only by transverse waves.
As fringe width is proportional to the wavelength and wavelength of light is inversely proportional to the refractive index of the medium,
Here,
$\lambda_\text{M}=\frac{\lambda}{\eta}$
$\lambda_\text{M}$ = wavelength in medium
$\lambda$ = wavelength in vacuum
$\eta$ = refractive index of medium
Hence, fringe width decreases when Young's double slit experiment is performed under water.
The corpuscular theory of light is proposed by newton in $1704$. It is referred as particle theory or newton’s theory of light.
According to this theory,
Light is made up of tiny particles called corpuscles having negligible mass. These particles $($corpuscles$)$ are perfectly elastic.
These tiny particles always travel in straight line in all directions.
These corpuscles ravel at very high velocity.
These corpuscles are of different sizes. The different color of light is due to different sizes.
Polarisation of light establishes that light are transverse in nature, otherwise it was believed that they are longitudinal waves, like the sound waves.
Light shows photoelectric effect and Compton effect, which depicts its particle nature. It also shows interference and diffraction, which depicts the wave nature of light.
Fringe width, $\beta=\frac{\lambda\text{D}}{\text{d}}$
Wavelength of red light is greater than wavelength of violet light; so, the fringe width will reduce.
Key concept:
Diffraction of Light is the phenomenon of bending of light around the comers of an obstacle/aperture of the size of the wavelength of light.
Size of the slit is very large compared to wavelength
Size of the slit is comparable to wavelenght
In figure $(A)$, no diffraction phenomenon is observed as the size of slit is weary large compared to wavelength. But in figure$(B),$ there will be diffraction of light as size of slit is compared to the wavelength of light incident.
Here in the question it is given, width of the slit
$\text{b}=10^4\mathring{\text{A}}=10^4\times10^{-10}\text{m}$
$=10^{-6}\text{m}=1\text{pm}$
Wavelength of $($visible$)$ sunlight varies from $4000\mathring{\text{A}}\text{ to }8000\mathring{\text{A}}$.
Hence the width of slit is comparable to that of wavelength, hence diffraction occurs with maxima at centre. So, at the centre all colours appear, i.e., mixing of colours form white patch at the centre.
When ordinary $($unpolarised$)$ light is reflected from a surface, it gets partial polarisation, it means some of the electric vectors in some planes are cut$-$off. When this partially polarized light is incident on polarized glasses, glass acts as an analyser and therefore block out some reflected light.
In $1678$, Dutch physicist, Christian Huygens, believed that the light was made up of waves vibrating up and down perpendicular to the direction of the light travels and therefore formulated away of visualising wave propagation.
This becomes know as Huygens principle. Huygens theory was the successful theory of light in three dimensions. Huygens suggested that the light wave peaks form from surfaces like the layers of onion. In a vacuum or other uniform mediums the light waves are spherical and these wave surfaces advance or spread out as they travel at the speed if light.
This theory explains why light shining through a pinhole or slitwall spread out rather than going in straight lines.
The image formed by the Compound microscope and Astronomical telescope is inverted,but in case of Simple microscope it form erect image.
On writing the given equation in the plane equation form $lx + my + nz = p,$
Where $l^2+m^2+n^2$ and $p>0$, we get:
$\frac{1}{\sqrt{3}}\text{x}+\frac{1}{\sqrt{3}}\text{y}+\frac{1}{\sqrt{3}}\text{z}=\frac{\text{c}}{\sqrt{3}}$
If $\theta$ is the angle between the normal and $+x$ axis, then
$\cos\theta=\frac{1}{\sqrt{3}}$
$\Rightarrow\theta=\cos^{-1}\Big(\frac{1}{\sqrt{3}}\Big) $
Frequency of a light wave doesnt change on changing the medium of propagation of light.
The phenomenon of rotation of plane polarized light is called optical activity.
When an object moves away from us, its light waves are stretched into lower frequencies or longer wavelengths, and we say that the light is redshifted.
It also explain the expanding nature of universe. Shifting towards red end means wavelength is increasing. There, milkyway is receding away from earth.
Interference effect is produced by a thin film $($coating of a thin layer of a translucent material on a medium of different refractive index which allows light to pass through it$)$. ln the present case, oil floating on water forms a thin film on the surface of water, leading to the display of beautiful colours in daylight because of the interference of sunlight.
Corpuscles are single, infinitesimally small, particles which have shape, size, color, and other physical properties.
Among the given sources, laser is the best coherent source providing monochromatic light with constant phase difference.
waves front are plane perpendicular to the direction of rays.
so, as light is traveling along $y -$ axis, plane perpendicular to $y -$ axis is the $x-z$ plane with any constant value of $y.$
so, $y =$ constant is the wave front plane
The locus of the equal path difference consists in lines going parallel to the axis of cylinder.
Therefore, interference fringes will be straight.
For interference to take place the light sources need to be either in phase or have a constant phase difference. In case the phase difference keeps changing the interference pattern will keep on changing, as a result of interference pattern will be observed.
When a drop of oil is spread on a water surface, it displays beautiful colors in daylight because the oil film is only a few nano-meters thick. Some of the light is reflected off the top surface and some the bottom surface. Because the thickness of the oil film is about the same as the wavelength of the light the two reflected rays interfere with each other.
Resolving power of a telescope $=\frac{\text{a}}{1.22\lambda}$
where a is the aperture of the telescope.
Thus resolving power∝ aperture.
Hence, if the aperture of telescope decreases, the resolving power decreases.
We know that, for the interference pattern to be formed on the screen, the sources should be coherent and emits lights of same frequency and wavelength.
In a Young's double$-$slit experiment, if one of the holes is covered by a red filter and another by a blue filter, then only red and blue lights are present due to alteration. In Young's double$-$slit experiment, a monochromatic light is used for the formation of fringes on the screen.
Therefore, there shall be no interference fringes.
Due to the large distance, the radius of the wavefront can be considered as large $($infinity$)$ and hence, a wavefront is almost plane.
As the intensity from second slit decreases the bright fringe becomes darker due to constructive interference and dark fringe becomes bright due to destructive interference.
It is the imaginary surface representing corresponding points pf a wave that vibrate in unison. When identical waves having a common origin travel through a homogeneous medium, the corresponding crests and troughs at any instant phase.
Huygen's wave theory explain the propagation of the wave front.
Unequal width of slits will cause unequal intensity of lights entering from both slits.
As a result, during interference complete cancelling of light intensity will not take place at regions of otherwise dark fringe.
As the value of $\beta$ does not depend on intensity of light, there will be no shifting of fringes as well as no change in fringe width.
Frequency of a light wave, as it travels from one medium to another, always remains unchanged, while wavelength decreases.
Decrease in the wavelength of light entering a medium of refractive index $\mu$, is given by,
$\lambda_\text{M}=\frac{\lambda}{\mu},$
Where $\lambda_\text{M}$ = wavelength in medium
$\lambda =$ wavelength in vacuum
$\mu =$ refractive index
Only transverse waves can exhibit polarization.
Light waves are transverse waves whereas sound waves are longitudinal waves, hence sound waves can not be polarized.
The setup shown is that of Young's Double Slit Experiment.
The fringe width in the experiment is given as $\beta=\frac{\text{D}\lambda}{\text{d}}$
where d is the distance between the slits, $D$ is the distance between screen and slits.
Hence the central fringe also widens when distance between screen and slits increases.
Since power of resolution is more for violet than for red, we conclude that resolving power is greater for light with lower wavelengths.
Wavelength of sodium light is around 589nm.
Hence resolving power increases for light with lower wavelength.
The Rayleigh criterion is the generally accepted criterion for the minimum resolvable detail $-$ the imaging process is said to be diffraction$-$limited when the first diffraction minimum of the image of one source point coincides with the maximum of another.
On the introduction of a transparent sheet in front of one of the slits, the fringe pattern will shift slightly but the width will remain the same.
A point source produces a spherical wavefront that moves in all the directions from the point.
Whereas the intensity at the wavelength is dependent on the distance and it follows the inverse square law. So, the intensity decreases with an increase in the distance from the source.
Intensity is proportional to the area of the slit.
As slit widths are in the ratio of $1:9$
The areas are also in the ratio $1:9$
Thus Intensities are in the ratio $1:9$
amplitudes are square root of Intensities
Thus amplitudes are in ratio $1:3$
Let amplitudes be x and $3x$
At maxima the amplitudes get added up $x + 3x = 4x$
At minima they become $x − 3x = −2x$
Intensity of maxima to minima is $\frac{16\text{x}^2}{4\text{x}^2}=\frac{4}{1}$
In optical instruments, the lenses are used to form images by Refraction.
When the yellow light of sodium lamp interferes constructively we get yellow bright band, and when they interfere destructively we get black bark band.
The speed of the current in the conductor is the same as the speed of light in the vacuum which is $3\times 10^8$
$\frac{\text{m}}{\text{s}}$
Conceptual, anti node represents joining of all points in constructive interface as the amplitude is high.
As the star coming closer to the earth, the frequency of the light increase and the wavelength decrease due to doppler effect. So the colour should gradually change to blue.