Let the width of the slit be divided into n equal parts so that
Now,
At this angle, each slit will make the first diffraction minimum. therefore the resultant intensity for all the slits will be zero at the angle of .

The superposition principle comes from the linear character of the differential equation of wavemotion.that is if and are the solution of any wave equation, then linear combination of and is also the solution of the wave equation.

When a low flying aircraft passes overhead, we notice slight shaking in pictures of the TV. This is because aircraft interferes with signals and reflects it. So the shaking we see is the interference of direct signal and reflected signal.

Given
Distance of screen from the slit,
Distance of first minimum
The wavelength of the light
Now,
As we know,
Hence, the width of the slit is 0.2 mm.

Given,
Distance between two towers = 40km
size of aperture =
Now,
As we know
Fresnel's distance is equal to half of the distance between towers
Also from the formula:
Hence this is the required longest wavelength of the radio wave, which can be sent in between the towers without considerable diffraction effect.

Typical size of the obstacle is much larger than the wavelength of light. Hence the diffraction effect is negligibly small. thus the assumption that light travels in a straight line can be safely used in day to day life.

The size of obstacle should be comparable to the wavelength for diffraction of waves by obstacles, through a large scale.
This comes from
This implies
it means the light goes almost unbent and hence student are unable to see each other.

A bright spot is seen at the centre of the shadow of the obstacle because wave diffracted from the edge of a circular obstacle interfere constructively at the centre of the shadow producing the bright spot.

When we have a width in the order of , the intensity of interference fringes in Young's double-slit experiment is modified by the diffraction pattern of each slit.

As we know,
width of the central diffraction band is given by
where d is the width of the slit.
So when we double the width of the slit, the size of the central diffraction band reduces to half of its value. But, the light amplitude becomes double, which increase the intensity 4 times.

Given,
Wavelength of light = 600nm
Angular fringe width
Hence spacing required between the two slits is .

The sound wave requires a medium for propagation.so, even though both given situation may relate to the same relative motion, they are not identical physically since, the motion of the observer, relative to the medium is different in two situations. Hence, we cannot expect the Doppler formula to be identical in both given cases.
When light waves are in a vacuum, there is clearly nothing to...

The speed of light in any medium depends upon the wavelength of the light and does not depends on the nature of the source, direction of propagation, the motion of the source and/or observer, and intensity of the wave.

The speed of light in a vacuum is constant and independent of anything according to Einstein's theory of relativity.

Let an object M is placed in front of a plane mirror AB at a distance r .
A circle is drawn from the centre, such that it just touches the plane mirror at point P. according to the Huygens’ principle, AB is the wavefront of the incident light .
If the mirror is absent then a similar wavefront A'B' would form behind M at a distance r.
A'B' can be considered as a virtual reflected ray...

According to corpuscular theory, when corpuscle of the light goes from rare medium to denser medium, the component of their velocity along the surface of the interface remains the same.
So we can write
As ,
That is light should be faster in the dense medium than in rare medium.this is the opposite of what we see experimentally.
Huygens wave theory predicts that light is faster in a rare...

Given,
wavelength Hα line emitted by hydrogen:
star is red-shifted by
let velocity of the star be
Now,
as we know,
from here
Hence speed at which star is receding away is

Given
Aperture
Wavelength of light
Now,
Distance for which ray optics is a good approximation also called Fresnel's distance:
Hence distance for which ray optics is a good approximation is 40m.

Given,
Wavelength of light
Speed of light
Now,
Wavelength and frequency will be the same when the ray is reflected.
Frequency of reflected light
Hence wavelength and frequency of light is and respectively.
Now,
as per the law of reflection, angle of incidence is always equal to angle of reflection .
Now, when the reflected ray is perpendicular with incidence ray,
Hence the angle...

Given,
Refractive index of glass
Now as we know,
where is the polarizing angle, also called the Brewster angle.and is the refractive index.
so from here
Hence Brewster angle is .

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