Question

Unpolarized light of intensity I0 is incident on a series of three polarizing filters. The axis of the second filter is oriented at 45o to that of the first filter, while the axis of the third filter is oriented at 90o to that of the first filter. What is the intensity of the light transmitted through the third filter

Answer 1

The intensity of the light transmitted through the third filter is
`I_3 = (I_o)/(8)`

Step-by-step explanation:

From the question we are told

The intensity of the unpolarised light
`I_o`

The angle between the first and second polarizer is
`\theta _1 = 45^o`

The angle between the first and third polarizer is
`\theta _2 = 90^o`

Generally the intensity of light emerging from the first polarizer is mathematically represented as

`I_1 = (I_o)/(2)`

According to Malus law the intensity of light emerging from the second polarizer is mathematically represented as

`I_2 = I_1 cos^2 (\theta_1)`

Substituting for
`I_1` and
`\theta _1`

`I_2 = (I_o)/(2) cos^2 (45)`

`I_2 = (I_o)/(4 )`

According to Malus law the intensity of light emerging from the third polarizer is mathematically represented as

`I_3 = I_2 cos ^2 (\theta_2 - \theta_1)`

Substituting for
`I_2` and
`\theta _1 \ and \ \theta _2`

`I_3 = (I_o)/(4) cos ^2 (90 - 45)`

`I_3 = (I_o)/(8)`