Answer :

A. Unpolarized light is a beam of light where the vibration of light vectors are in all directions in the plane which is perpendicular to direction of propagation of light whereas in linearly polarized light the vibration of light vectors is only in one direction in a plane which is also perpendicular to the direction of motion.

Polarized light can be distinguished from unpolarized light by using a polaroid. When a linearly polarized light is passed through a polaroid, it will only pass through the polaroid if the pass axis of polaroid is parallel to the light vector and there will be no change in the intensity when the polaroid is rotated.

Linearly polarized light can be obtained by a polarizer, the electric field vectors which are not parallel to the aligned molecules of the polarizer get absorbed and which are parallel are not absorbed thus a linearly polarized light is obtained.

B. Given: -

The intensity of the incident light I_{0}

Calculation: -

After passing the first polaroid P_{1} the intensity be I_{1}

We know that I_{1} reduces to half After passing the third polaroid P_{2} the intensity be I_{2} We can write by malus’ law as,

Where, I_{0} is the intensity of incident light and = 60^{o} is the angle between the pass axis of P_{1} and P_{2}

So, the intensity of light passed through P_{2} is,

Conclusion: -

the intensity of light after passing through P_{2} is,

**OR**

A.

B. Given: -

Wavelength of light, λ = 500 nm

Width of the single slit, a = 0.2 mm

Distance between the double slits, d= 0.5 mm

Formula: -

In a diffraction obtained through single slit,

The angular width of the central maxima (ω) is given as,

And linear width of the central maxima (ω’) is given as,

In Young’s double-slit experiment,

The fringe width (β) is defined as,

Where λ is the wavelength of the light is used for diffraction/interference, and a is the width of the single slit, d and D is the distance between the slits, and sources and the screen respectively in Young's double-slit experiment,

Calculations: -

Substituting the values given in the above formula we get,’

ω = 5 × 10^{-3} radians

Also, the linear width is

Given that maximum fringes in young double slit expression that fit the same length is n,

Also, width of one fringe is,

So total length is, nβ, which gives,

nβ = ω’

So, n = 5

Conclusion: -

Hence, the angular width of the central maximum is, ω = 5 × 10^{-3} radians.

And the number of fringes obtained in Young's double-slit experiment, accommodated within the region of total angular spread of the central maximum due to single slit is n = 5.

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