Question

Unpolarized light is incident upon two ideal polarizing filters that do not have their transmission axes aligned. If of the light passes through this combination, what is the angle between the transmission axes of the two filters

Answer 1

The angle between the transmission axes of the filters is 65°

Step-by-step explanation:

The complete question is

Unpolarized light is incident upon two ideal polarizing filters that do not have their transmission axes aligned. If 18% of the light passes through this combination, what is the angle between the transmission axes of the two filters.

From Malus law,

`I = I_(0) cos^(2) \beta` ....1

where
`I` is the intensity of the polarized light,

`I_(o)` is the intensity of the incident light

β the angle between the transmission axes of the two filters

Since the intensity is reduced to 18% or 0.18 of its initial value, this means that

`cos^(2) \beta` = 0.18

substituting into the equation above, we have

`I = 0.18I_(0)` ....2

equating the two equations, we have

`I_(0)cos^(2) \beta` =
`0.18I_(0)`

`cos^(2)\beta` =
`(0.81I_(0) )/(I_(0) )` = 0.18

`cos \beta` =
`√(0.18)` = 0.424

`\beta` =
`cos^(-1) 0.424` = 64.9 ≅ 65°