23) what value of theta would give I2/I0 =0.5? Answer is A 24) what value of the

Question

23) what value of theta would give I2/I0 =0.5? Answer is A

24) what value of theta would give I2/I1= 0.75? Answer is C/

Please help #23, 24! I need solution. Thanks

Physics 212A Exam II Fall 2012. The next two questions pertain to the situation described below. A beam of unpolarized light travels in the +z-direction and is incident on two linear polarizers of intensity lo below. The transmission axis of LP1 makes (LP1 and as shown the an angle of 25° relative to the x-axis, while the angle between the TA of LP2 and x-axis is unknown. The light in Regions Iand II has intensities 11 and h, respectively. unpolarized beam 250 TA. TA Region I LP1 Region II LP2 23. What value of 0 would give hll 0.5? COS RSCOS 25° b. 57.5 c. 0 20° 24. What value of 0 would give h/II 0.75? CO on

Explanation / Answer

at first polarizer, as the incident light is unpolarized, light coming out of LP1 will be 0.5 times original intensity(using Malus law)

hence I1=0.5*I0

for light coming out of LP2,

iintensity will be cos^2(angle between two axes) times the intensity incident on LP2 which is I0/2

so net intensity I2=0.5*I0*cos^2(t)

where t=angle between two axies

=theta-25

Q23.

I2/I0=0.5*cos^2(theta-25)

==>0.5=0.5*cos^2(theta-25)

==>theta-25=0

==>theta=25 degrees

hence option a is correct.

Q24.

I2/I1=cos^2(theta-25)

==>0.75=cos^2(theta-25)

==>cos(theta-25)=0.866

==>theta-25=30 degrees

==>theta=55 degrees

but it is not given as an option

as we know cos(A)=cos(-A)

==>cos(theta-25)=cos(25-theta)

hence 25-theta=30

==>theta=25-30=-5 degree

hence option C is correct.

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