Three polarising filters are stacked with the polarising axis of the first filte

Question

Three polarising filters are stacked with the polarising axis of the first filter vertical, the second filter at 48.0 degree to the first, and the third filter at 90.0 degree to the first. An unpolarised light of intensity I0 is incident on the stack. (i) What is the intensity of light emerging from the first filter? (before entering the next filter) (ii) What is the intensity of light emerging from the second filter? (before entering the next filter) (iii) What is the intensity of light emerging from the third filter? (iv) If the second filter is removed, what is the intensity of the light emerging from the last filter?

Explanation / Answer

Let the 3 polarisers be: 1, 2 and 3

Unpolarised light enters the filter 1 , then filter 2 and finally filter 3.

Intensity of unpolarised light = I0

Intensity of unpolarised light after passing through any polarising filter becomes = I0 /2

(i) Thus Intensity of light after emerging from filter 1 and befor entering 2nd filter is I1 = I0 / 2

Now according to Law of Malus when a polarised light enters a filter that is oriented at an angle (theta), then the light intensity after passing through the filter becomes:

I' = I2 cos2(theta)

(ii)

Here filter 2 is oriented at angle = 48 degrees to filter 1.

Now I1 = I0 /2 passes through filter 2, the intensity of light after emerging from filter 2 and before entering filter 3 becomes:

I2 = I1 cos2 (48) = I1 * 0.448

Thus I2 = 0.448 I1 = 0.448 I0 /2 = 0.224 I0

(iii) The third filter is at 90 deg with respect to 90 1st filter and filter 2 is at 48 with respect to filter 1. Thus,

The filter 3 is at (90-48) = 42 degrees with respect to filter 2.

The light intensity emerging from filter 3 is:

I3 = I2 cos2 (42) = 0.55 I2 = 0.55 * 0.224 I0 = 0.124 I0

Thus, I3 = I0 cos2 (90) = 0

(iv) Now we remove the second filter and are left with 2 filters only: 1 and 3 that are perpendicular to each other. Now the light intensity I1 = I0/2 is falling on filter 3. Intensity of light after emerging from filter 3 becomes:

I3' = I1 cos2 (90) = 0

Light intensity from 2 filters that are perpendicular to one another is Zero.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.