Physics 2049 Spring 2005
Quiz 8
Name:
Period:
Question 1 (3 points)
It is a commonly accepted that the universe is undergoing a spherically symmetric expansion such that
the physical distance between any two points is given by r(t) = a(t)l0 where l0 can be taken as the initial
separation and a(t) is the “expansion” factor. If an observer at time t1 observed an intensity I from an
astrophysical light source of power P , what is the ratio of expansion factors if an observer at some later time
t2 observes an intensity twenty times weaker than I? (Hint: we make a crude assumption that the power of
light sources in the universe remains constant over time)
The intensity at any time is given by,
P
I=
.
4πr2 (t)
Since r(t) = a(t)l0 , the ratio of intesities given is,
I1
a(t2 )2
=
= 20 ,
I2
a(t1 )2
and therefore,
√
a(t2 ) √
= 20 = 2 5 .
a(t1 )
Question 2 (3 points)
A beam of polarized polarized light is sent into a system of two polarizing sheets. Relative to the polarization
direction of that incident light, the polarizing directions of the sheets are at angles θ for the first sheet and
90◦ for the second sheet. If 10% of the incident intensity is transmitted by the two sheets, what is θ?
Since the incident light is polarized, the intensity after the first polarizer is given by,
I1 = I0 cos2 θ .
After the light passes through the second polarizer the intensity is given by,
I2 = I1 cos2 (90◦ − θ) = I0 cos2 θ sin2 θ.
Therefore, the ratio of intensities gives,
1
1
I2
=
= I0 (2 cos θ sin θ)2 ,
I0
10
4
1
= sin2 2θ,
4
Ãr !
1
2
−1
θ = sin
≈ 20◦ .
2
5