# Minqi 19 May 2016 - 1

## Question

A beam of initially unpolarised light passes through three polaroids P, Q and R. Polaroid P's axis of polarisation is vertical. Which orientation of polaroids Q and R with respect to the vertical axis will produce an emergent beam from polaroid R with maximum intensity.

Orientation with respect
to the vertical axis

Q         R
A     45o      45o
B     45o      90o
C     90o      180o
D     180o     60o

When a wave polarised in one axis passes through another polaroid with the axis at an angle of θ, only the component of the wave parallel to the new axis can pass through.

A1 = A0 cos θ

After passing through the second polaroid placed at an angle of ϕ, the final amplitude will be given by

A2 = A1 cos ϕ

Hence, the final intensity will be given by

A2 = A1 cos ϕ
= ( A0 cos θ ) cos ϕ

I2 = k ( A 2 )2
= k ( A0 cos θ cos ϕ )2
= k A02 cos2 θ cos2 ϕ
= I0 cos2 θ cos2 ϕ

For option A,
I2 = I0 cos2 θ cos2 ϕ
= I 0 cos2 45 o cos2 (45o - 45 o)
= 0.50 I0

For option B,
I2 = I 0 cos2 θ cos2 ϕ
= I0 cos2 45o cos2 (90o - 45o)
= 0.25 I0

For option C,
I2 = I0 cos2 θ cos2 ϕ
= I0 cos 2 90o cos2 (180o - 90o)
= 0

For option D,
I2 = I0 cos2 θ cos2ϕ
= I0 cos2180o cos2(180o - 60o)
= 0.25 I0

Hence, Option A will produce a beam with maximum intensity.