Light that is polarized along the vertical direction is incident on a sheet of polarizing material. Only 94% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes through the second sheet. What angle does the transmission axis of the second sheet make with the vertical?
The solution is almost correct, except that for the final answer it would be 90 + 14.18 = 104.18 degrees because the first sheet is already rotated 14.18 degrees from the vertical.
No, the correct answer is 90 + 14.18 = 104.18
If no light gets through the second material, it must be passing only light polarized in the horizontal direction (perpendicular to the "transmission axis") of the first sheet.
We can use Malus law to solve this problem, equaiton 24.7:
S=Socos2Θ
S=amount of light leaving
So = amount of light entering
We know that S/So = 94%, or 0.94
Now, to solve for Θ from Malus law
S/So =cos2 Θ
Θ=cos-1 sqrt (S/So)
Θ= cos-1 sqrt (0.94)
Θ= 14.18
We subtract this from 90 due to respct to the vertical
so 90-14.18= 75.82 degrees
My apologies: the range for Θ is between 0 and 90 degrees, so the original answer of 75.82 degrees is correct.
Both are correct. One (~75) rotates the opposite direction of the original rotation and one continues in the same direction (~104). The question asks the angle to the vertical.
To determine the angle that the transmission axis of the second sheet makes with the vertical, we need to understand how two polarizing sheets interact with polarized light.
When polarized light passes through a polarizing material, it gets filtered based on the orientation of its electric field vector. If the polarization direction of the light matches the transmission axis of the polarizing material, the light can pass through with maximum intensity. However, if the polarization directions do not align, the intensity of the light passing through will decrease.
Let's break down the problem step by step:
1. The incident light is polarized along the vertical direction. This means that the electric field vector of the light oscillates vertically.
2. The first sheet of polarizing material transmits only 94% of the intensity of the incident light. This tells us that the transmission axis of the first sheet is not aligned with the vertical direction.
3. Now, the partially transmitted light strikes the second sheet of polarizing material. We are told that no light passes through the second sheet. This means that the transmission axis of the second sheet is perpendicular to the polarization direction of the incident light.
4. The angle that the transmission axis of the second sheet makes with the vertical can be determined by recognizing that the transmission axes of the two sheets are perpendicular to each other.
So, the transmission axis of the second sheet is horizontal, making a 90-degree angle with the vertical direction.