Wave Optics Test - 6

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
 
n₁ sin θ₁ = n₂ sin θ₂
1 x sin35^o =1.48sin θ₂
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, n λ= xd/D

⇒d= n λD/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 νgives the same λ. for the two light sources.
Example: y₁ ​=A₁ ​sinwt and y₂ ​=A₂ ​sin(wt+ϕ) where ϕis constant.

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