Physics, 14.04.2020 16:52 yuhhhhh2801

Imagine you have two identical perfect linear polarizers and a source of natural light. Place them one behind the other and position their transmission axes at 0 and 50 degrees respectively. Now insert between them a third linear polarizer with its transmission axis at 25 degrees. If 1000 W/cm2 of natural light is incident, how much will emerge with and without the middle polarizer in place?

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Without the third polarizer inserted in the middle of the first and second polarizer the irradiance of light that would emerge from the second polarizer is

I_2=321.39 W/cm^2

With the insertion of the third polarizer at the middle of the first and second polarizer the irradiance of light that would emerge from the second polarizer is

$I_4 = I(\theta_d_1) = 337.3 W/cm^2$

Explanation:

From the question we are told that the

The angle between the transmission axis of first linear polarizer and the vertical axis is $\theta_1 = 0^o$

The angle between the transmission axis of second linear polarizer and the vertical axis is $\theta_2 = 50^o$

The angle between the transmission axis of third linear polarizer and the vertical axis is $\theta_2 = 25^o$

The irradiance of the incident natural light is I = 1000 W/cm^2

Generally a linear polarizer divides the irradiance of a natural light by 2

So For the first polarizer the irradiance of the natural light would become

$I_1 = \frac{I}{2}$

Substituting values

$I_1 = \frac{1000}{2}$

$=500 \ W/cm^2$

Now looking at the question we can deduce that the angle between the transmission axis of the and second polarizer is

$\theta_d = \theta _2 - \theta_1$

Substituting values

$\theta_d = 50^o - 0^o$

=50^o

According to Malus Law the irradiance of light that would come out from the second polarizer is obtained by this mathematical expression

$I(\theta_d) = I_1 cos^2(\theta_d)$

Substituting values

$I_2 = I(\theta_d) = 500 *cos (50)$

=321.39 W/cm^2

When the third polarizer is inserted between the first and second polarizer, we have that

The angle between the first polarizer and the third polarizer is mathematically evaluated as

$\theta_d_1 = \theta_3 - \theta_1$

Substituting the values

$\theta_d_1 = 25^o -0^o$

= 25^o

According to Malus Law the irradiance of light that would come out from the third polarizer is obtained by this mathematical expression

$I(\theta_d_1) = I_1 cos^2(\theta_d_1)$

$I(\theta_d_1) = I_1 cos^2 (25)$

Substituting values

= 500 cos^2(25)

$I_3 = I(\theta_d_1) = 410.69 W/cm^2$

The angle between the third polarizer and the second polarizer is mathematically evaluated as

$\theta_d_2 = \theta_2 - \theta_3$

Substituting the values

$\theta_d_2 = 50^o -25^o$ [Note the third polarizer is placed at the

= 25^o The middle of the first and second

polarizer

According to Malus Law the irradiance of light that would come out from the second polarizer is obtained by this mathematical expression

$I(\theta_d_2) = I_3 cos^2(\theta_d_2)$

$I(\theta_d_1) = I_3 cos^2 (25)$

Substituting values

= 410.69 cos^2(25)

$I_4 = I(\theta_d_1) = 337.3 W/cm^2$

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