Question

You have an unpolarized light source and you wish to send a beam of this light with intensity Io through a number of sheets of polarizing material. You stack the sheets of polarizing material so that the axis of polarization for the last sheet is always at right angles to that of the first sheet and the transmission axis of each sheet relative to the preceding sheet is the same for every sheet. Determine the following (a) the intensity I3 of the light (in terms of I transmitted through a stack if the stack consists of three sheets of the polarizing material By what fraction is the intensity of light reduced by the first filter? How is the intensity of light after the second filter related to that after the first filter? How can you determine the angle between adjacent polarizing fters?Io (b) the intensity I4 of the light (in terms of ) transmitted through a stack if the stack consists of four sheets of the polarizing material How can you modify your work from part (a) in order to solve part (b)?Io (c) the intensity 20 of light (in terms of I) transmitted through a stack if the stack consists of twenty sheets of the polarizing material 20 How can you modify your work from part (a) in order to solve part (c)Io (d) an expression for the intensity I, of light (in terms of Io) transmitted through a stack if the stack consists of n sheets of the polarizing material 90.0 2(n - 1) が10 cos( 90.00 )2(n-1) 90.0° 2(n -1) 90.0 2n

Answer 1

Step-by-step explanation:

a ) The angle between the polarization axis of two adjecent sheet

= 90 / 3 = 30 degree.

The formula for intensity of polarised light from unpolarised light ( first transmission

I₁ = I₀ /2

I₀ is intensity of unpolarised light and I₁ is intensity of light after first time polarization .

The relation of I₁ and I₂ is as follows

I₂ = I₁ cos²30

= I₀/2 x3/4

=3 I₀/8

Relation between I₃ and I₂ is as follows

I₃ = I₂ cos²30

= 3I₀ / 8 x 3/4

= 9 I₀ / 32

= 0 .28 I₀

In case of stack of 4 plates

angle between two plates = 90/4 = 22.5 degree

I₁ = I₀ /2

I₂ = I₁ cos²22.5

= I₀ /2 x .85

I₃ = I₂ cos²22.5

= I₀ /2 x .85 x .85

= .36 I₀