Transcript HW#2 answers

Homework #2
2/5/13
Light equations - transparent objects
• Fraction light reflected
(for normal incidence)
• Fraction light transmitted
2
æn1 - n2 æ
fR = æ
æ
n
+
n
æ 1 2æ
I
fT = = exp(-e Cl ) = exp(-a l )
I0
• Fraction light absorbed
fT + fR + fA =1
f = 1A
fT - fR
1a. Three beams
Reflected beam
Incident beam
Refracted beam
Reflected beam moves since reflected angle = incidence angle
and refracted angle is set by Snell’s law
1b) You lose refracted beam at
critical angle
n1 sinq1 = n2 sinq 2
At critical incident angle…
• the refracted beam is 90° and for
larger incident angles there is only
reflection
Total internal reflection
n1 sin q crit = n2 sin 90 = n2
n2
1
sin q crit = =
n1 1.5
q crit = 42
Snell’s law
1c. Index of refraction varies with λso
angle of refraction varies with λ
1d. Index of refraction = speed of light in
vacuum / speed of light in material
So speed of light in material = 1/n * c= 1/1.5*c = 0.67 c
1e. Two angles
Angle of incidence (50°) = angle of reflection (50°)
Angle of refraction from Snell’s law
q2 = sin -1 (n1 sinq1 / n2 ) = sin -1 (1*sin50 /1.5) = 30.7
1f. Reflected intensity vs angle
We can calculate the expect fraction of light reflected as
2
æn - n æ æ1-1.5 æ
fR = æ 1 2 æ = æ
= 0.04
æ
æ
æ
1+1.5
æn1 + n2 æ
2
Homework # 2 - Reflection
2. Eye reflection
2a. Reflection at air / cornea
2b. Reflection at aqueous
humour / lens
Doesn’t matter which material is 1 and 2
#2c. Eye glasses - no eyes
• 1st surface reflection
Glass
Air
2
ænglass - nair æ æ1.55 -1æ2
R1 = æ
=æ
= 0.046
æ
æ
ænglass + nair æ æ1.55 +1æ
R1
I0
• 2nd surface reflection
2
ænair - nglass æ æ1-1.55 æ2
R2 = æ
=æ
= 0.046
æ
æ
ænair + nglass æ æ1+1.55 æ
R1 + R2 = 0.046 + 0.046 = 0.092
R2
I1
I2
#1c. Eye glasses - no eyes
• First surface reflection
Glass
Air
R1 = R2 = 0.046
R1
• If we ignore absorption
I1=(1-R1) * I0 = 0.95 I0
I0
R2
I1
• 2nd surface reflection
I2 = (1-R2) * I1
= (1-R1)*(1-R2) * I0 = 0.909
So total reflection is Rtot= 1 - I2 = 1-0.909 =
0.091
I2
3. Snell’s law
3a. Refraction at air / cornea
3. Snell’s law
3a. Refraction at air / cornea
3b. Refraction at aqueous humour / lens
So light bends most at
----The cornea - 80% of focusing
Comparison of bending at cornea
and lens
Bending at cornea
24° - 17.2° = 7.8°
Bending at lens
24° - 22.7° = 1.3°
Homework #4a - photons in a laser
• 650 nm laser
E (photon) = 3 x 10-19 J
Laser power = 1 mW = 0.001 J/s
# photons/s = laser power / photon energy
= 0.001 J / s / 3 x 10-19 J
= 3 x 1015 photons / s
#4b - Absorption
0
• Transmission = 1 – Absorption - Reflection
fT = I / I0 = 90%
Absorption = 1 - fT
= 1 - 0.9 = 0.1
#4b - Absorption
0
• Transmission = 1 – Absorption - Reflection
fT = I / I0 = 90%
Absorption = 1 - fT
= 1 - 0.9 = 0.1
# photons absorbed = 0.1 * (# photons from
laser)
= 0.1 * (3 x 1015 photons/s)