Test: Wave Optics

Explanation:explanation none

We know that,
Phase difference=K× path difference. K=2π/ λ.
Therefore, phase difference=(2π/ λ) ×( λ/3)=2π/3=120 degree.

Brewster's angle is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized.

(a) Speed of light in glass is c/μ=2×10⁸m/s

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

When we use white light, the central bright will have light from all wavelengths as none of them cancel out. Hence the central bright fringe appears white.
For other bright fringes, depending on the wavelength of light constructive interference will not take place for certain wavelengths. Hence they will not be white, rather will be coloured, hence differentiated from central fringe.

Light as a wave: Light can be described (modeled) as an electromagnetic wave. In this model, a changing electric field creates a changing magnetic field. This changing magnetic field then creates a changing electric field and BOOM - you have light. Unlike many other waves (sound, water waves, waves in a football stadium), light does not need a medium to “wave” in.

The process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge, typically accompanied by interference between the waveforms produced.

The shape of the wave front in case of a light diverging from a point source is spherical and is shown in the given figure. The shape of the wavefront in case of a light emerging out of a convex lens when a point source is placed at its focus is a parallel grid.

Distance between the slits, d=0.28×10⁻³ m
Distance between the slits and the screen, D=1.4m
Distance between the central fringe and the fourth (n=4) fringe, 
u=1.2×10⁻² m
In case of a constructive interference, we have the relation for the distance between the two fringes as:
u=nλD/d
⇒λ=ud/nD=6×10⁻⁷m=600nm

Distance between the slits, d=0.28×10−3 m

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

Distance between the central fringe and the fourth (n=4) fringe, 

u=1.2×10−2 m

In case of a constructive interference, we have the relation for the distance between the two fringes as:

u=nλD/d

⇒λ=ud/nD=6×10−7m=600nm

Diffraction is defined as the process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge, typically accompanied by interference between the waveforms produced.

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

 Answer :- d

Solution :- Let at liner distance 'y' from center of screen the bright fringes due to both wavelength coincides. Let the n1 number of bright fringe with wevelength λ1 coincides with n2 number of bright fringe with wavelength λ2

We can write

y = n1​β1 = n2β2

n1 = λ1D/d                = n2​Dλ2/d                 or n1λ1=n2λ2

​Also at first position of coincide the th bright fringe of one will coincide with (n+1)th bright fringe of other.

If λ2<λ1,

So, then n2>n1

 and n2 = n1+1

Using equation (ii) in equation (i)

n1λ1=(n1+1)λ2

​n1(650)×10^−9 = (n1+1)520×10^−9 

65n1 = 52n1 + 52 or 12n1 = 52or n1=3

Thus, y = n1β1 = 3[(6.5×10^−7)(1.2)]/2×10^−3 = 1.17×10^−.3

m=1.17mm

We know that,
Wavelength of light in a material:
λ= λ₀/n
where, λ=wavelength of material, λ₀=wavelength of light in vacuum,
n=index of refraction of material.
So, 650x10^-9m/1.47=442.177nm.

The least distance from the central maximum where the bright fringes due to both the wavelengths coincide is 1.56 mm. This can be determined by using the equation `beta = (n lambda D)/(d)`, where `n` is the order of the fringe, `lambda` is the wavelength, `D` is the distance between the two slits, and `d` is the distance from the central maxima. Thus, `beta = (4 lambda D)/(d) = 1.56 mm`.

The angle of incidence = 90^∘ - 47.5^∘ = 42.5^∘
Now by snells’ laws we get 
sin r = sin 42.5^∘ / 1.66^∘
Thus we get r = 24.01^∘
Thus the angle with surface = 90^∘ -24.01^∘ = 65.99^∘

Plane (a small area on the surface of a large sphere is nearly planar). The portion of the wavefront of light from a distant star intercepted by the Earth is a plane.

The bright colors seen in an oil slick floating on water or in a sunlit soap bubble are caused by interference. The brightest colors are those that interfere constructively. This interference is between light reflected from different surfaces of a thin film; thus, the effect is known as thin film interference.

Every point on a wave-front may be considered a source of secondary spherical wavelets which spread out in the forward direction at the speed of light. The new wave-front is the tangential surface to all of these secondary wavelets.

According to Huygens' principle, a plane light wave propagates though free space at the speed of light, c. The light rays associated with this wave-front propagate in straight-lines. It is also fairly straightforward to account for the laws of reflection and refraction using Huygens' principle.

Here,
Aperture, a = 4 mm = 4 × 10-3 m
Wavelength, λ = 400 nm = 400 × 10-9 m = 4 × 10-7 m 

Ray optics is good approximation upto distances equal to Fresnel's distance (ZF).
Fresnel's distance is given by,

From air to liquid:
1 ->air
2->liquid
 
n₁sinθ₁= n₂sinθ₂
1 x sin35^o=1.48sinθ₂
θ₂=arcsin((1xsin35o)/1.48)=22.8^o

The Huygens-Fresnel principle states that every point on a wavefront is a source of wavelets. These wavelets spread out in the forward direction, at the same speed as the source wave. The new wavefront is a line tangent to all of the wavelets.
The correct answer is option B.

Wavelength of light beam, λ

Distance of the screen from the slit, D=1m

For first minima, n=1

Distance between the slits is d

Distance of the first minimum from the centre of the screen can be obtained as, x = 2.5mm = 2.5×10⁻³

Now, nλ = xd/D

⇒ d= nλD/x = 0.2mm

Therefore, the width of the slits is 0.2 mm.

A wave front is a line representing all parts of a wave that are in phase and an equal number of wavelengths from the source of the wave. A ray is a line extending outward from the source and representing the direction of propagation of the wave at any point along it. Rays are perpendicular to wave fronts.

Tan(90-i)=14/11.2
Cot i=14/11.2
I=cot-1(14/11.2)
I=39.4^o

In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency (amplitude may be different).
As c be the speed of light which is constant.
Using, c=νλ
Now the same ν gives the same λ. for the two light sources.
Example: y₁​=A₁​sinwt and y₂​=A₂​sin(wt+ϕ) where ϕ is constant.

Constructive interference occurs when the path differences (S₁​P−S₂​P) is an integral multiple of λ or (S₁​P−S₂​P)=nλ
Where n=0,1 ,2 3,….