Question

Horizontally polarized light reflecting off of a lake surface reaches a polarizer with a vertically oriented transmission axis. (a) What percentage of the original light intensity is transmitted through the polarizer? (b) If an additional polarizer (with its transmission axis oriented at an angle of 35 degrees from the horizontal) is placed in front of the original polarizer (so that the light reaches the new polarizer first), what percentage of the original intensity is transmitted through both polarizers? (c) If the incident light came directly from the sun rather than from the lake surface, what percentage of the original intensity would be transmitted through both polarizers? (d) In either case, if any light passes through both polarizers, would the magnetic field of the transmitted light waves be oscillating in a direction that is parallel to or perpendicular to the lake surface? Why?

Answer 1

from Malus's law I = I₀*cos²@

I = transmitted intensity

I₀ = original intensity

i) @ = 90

I = I₀*cos² ( 90)

= 0

0% of original light is transmitted through polarizer.

(ii) If second polarizer is placed in front of first polarizer .

@ = 35⁰

I = I₀*cos² ( 35) --------------------------1

Now while passing through next polarizer

@ = 90-35 = 55⁰

I' = I * cos²(55)

= I₀* cos² (35) * cos² (55) (from eq.1)

I' / I₀ = 0.671*0.3289

= 0.22075

22.075% of original intensity is transmitted through polarizer.

(iii) When incident light directly come from sun , then it will be unpolarized light.

If I₀ is the intensity of unpolarized light then

intensity of light fron first polarizer , I = I₀/2

from second polarizer , I' = I* cos²(55) ( @= 90-35 = 55)

= (I₀/ 2) * cos²(55)

I' / I₀ = 0.1644

16.44 % of original light intensity is transmitted through polarizer.