What is the intensity of the incident of light?

[phy112]

Homework Statement

Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of 28.0° with respect to the first and the third is oriented at an angle of 45.0° with respect to the first. If the light that emerges from the system has an intensity of 2.1 W/m2, what is the intensity of the incident light?

Homework Equations

is this what you do: 2.1W/m^2 divided by cos^2(21). then divide that answer by cos^2(28) than multiply that anwswer by 2? I can's eem to get the right anwser to cos2(21) and cos2(28) right in my calculator. I need some help

The Attempt at a Solution

 

[Redbelly98]

You're right except for the 21^o. What is the angle between the 2nd and 3rd polarizers?

(Good job catching the final 2x factor, a lot of people miss that on problems like this.)

 

[nlightner]

I would approach this problem by first understanding the concept of intensity of light. Intensity is defined as the amount of energy that is transferred per unit area per unit time. In this case, we are given the intensity of the light that emerges from the system, which is 2.1 W/m2. This means that for every square meter of area, 2.1 Joules of energy are being transferred per second.

To find the intensity of the incident light, we can use the Malus' law, which states that the intensity of light passing through a polarizer is proportional to the cosine squared of the angle between the polarization direction of the incident light and the axis of the polarizer. In this case, we have three polarizers, each at different angles, so we need to consider the cumulative effect of all three polarizers.

Using the given angles of 28.0° and 45.0°, we can calculate the intensity of the incident light as follows:

I = I_0 cos^2(21) cos^2(28) cos^2(45)

Where I_0 is the initial intensity of the incident light. Rearranging the equation, we get:

I_0 = I / (cos^2(21) cos^2(28) cos^2(45))

Plugging in the given intensity of 2.1 W/m2, we get:

I_0 = 2.1 / (cos^2(21) cos^2(28) cos^2(45))

Using a scientific calculator, I get the value of I_0 to be approximately 3.48 W/m2. This is the intensity of the incident light that is being transmitted through all three polarizers.