Question

if the plane of vibration of the incident ray make an angle 30 degree with the optic X is the ratio of intensities of ordinary and extraordinary rays are ​

Answer 1

Concept:

According to Malus' law, the intensity of plane polarised light passing through an analyser varies as the square of the angle's cosine formed by the planes polariser and the transmission axis of the analyser.

Given:

Incident ray is making angle of 30 degrees.

Find:

Ratio of intensities of ordinary rays to extra ordinary rays.

Solution:

Let us suppose the initial intensity of light is I₀

The final intensity of light according to malus law will be

I = I₀ cos² θ

where θ is the angle

So, by applying the formula the the final intensity of light will be

I = I₀ cos²30°

I = I₀ (√3/2)²

I = (3/4)I₀

Intensity of ordinary ray is I₀

Intensity of extra ordinary ray is (3/4)I₀

Ratio = Intensity of ordinary ray / Intensity of extra ordinary ray

Ratio = I₀ / (3/4)I₀

Ratio = 4/3

Hence, the ratio of intensities of ordinary ray to extra ordinary ray is 4/3.

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Answer 2

Answer:

Concept :

Light's polarisation characteristics are the subject of Malus' law. It aids in our understanding of the connection between light intensity and the polarizer-analyzer. He discovered that when sunlight is reflected off of a glass surface, it can become polarised. He carried out his investigation on a calcite crystal. After carrying out the experiment, he discovered that s- and p- polarisation, which are mutually perpendicular to one another, occurred in natural light. This law is used to explain how optics and electromagnetism are fundamentally related. This law also illustrates how electromagnetic waves are transverse in nature. Malus noticed that when the crystal was turned, the intensity changed from its highest to lowest point. In light of this, he suggested that the amplitude of the reflected beam must be A = A0 cos.

Explanation:

Given :

Incident ray is making angle of 30 degrees

To find :

Radio of intensities of ordinary rays to extra ordinary rays

Solution :

According to malus law the final intensity,

I = Io $cos^{2}$

I= Io $cos^{2}$ 30°

I= Io $(\frac{\sqrt{3} }{2}) ^{2}$

I= $(\frac{3}{4} )$ Io

Intensity of extra ordinary ray is $\frac{3}{4}$  Io

Ratio = intensity of ordinary ray/intensity of extra ordinary ray

Ratio=  $\frac{lo}{\frac{3}{4} }$ lo

Ratio= $\frac{4}{3}$

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