Question

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to 1515.

Answer 1

Complete Question

At what angle should the axes of two Polaroids be placed so as to reduce the intensity of the incident unpolarized light to 1/5.

Answer:

The angle is

Step-by-step explanation:

From the question we are told that

The light emerging from second Polaroid is 1/5 the unpolarized

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

`I_1 = (I_o)/( 2 )`

Generally from the Malus law the intensity of light emerging from the second Polaroid is mathematically represented

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

=>
`cos^2 (\theta ) = (I_2)/(I_1 )`

=>
`cos (\theta) = \sqrt{ (I_2)/(I_1) }`

From the question
`I_2 = (I_o)/(5)`

`cos (\theta) = \sqrt{ ( ( I_o)/(5) )/((I_o)/(2) ) }`

`cos (\theta) = \sqrt{ (2)/(5) }`

=>
`\theta = cos ^(-1) [\sqrt{(2)/(5)} ]`

=>
`\theta = 50.77^o`