Question

how many individual polarizers would you need to rotate a laser beams polarization axis by 90 degrees and lose only 5% intensity? what would be the relative angle between each polarizer

Answer 1

Using Malus' Law,

where, is the polarized light intesity

is the input light intesity

is the relative polarizer angle

so after first polarizer, we will have intensity as

so after second polarizer, we will have intensity as

so after nth polarizer, we will have intensity as

Thus we write this as:

.........EQ1

Now we know that only 5 % intensity is lost and total 90 degrees rotation polarization axis

So, substituting in EQ1 we get,

........... EQ2

Also, we know total angle rotation is 90^o

.................EQ3

Now we need to select value of n such that it fulfills EQ2 and and we will get the relative angle between each polarizer by EQ3

1	90	0
2	45	0.25
3	30	0.421875
48	1.85	0.949886
49	1.836735	0.950883

Note: use excel sheet to calculate the values

Answer:

So the number of polarizers needed is 49.

The relative polarizer angle is 1.8367^o.