1. Homework
Assignment #4
2/24/11

2. Ear’s adaptation to capture sound
1800 mm2
Sound in air must get into fluid filled cochlea
Amplification
Pressure = force / area
As area decreases, pressure increases a) b)
3.2 mm2
70 mm2

3. Additional factors C) 30% more force from levers of middle ear bones
25.7*21.8*1.3 = 731
D) Round window decreases resistance
731 * 4 = 2925
This is nearly 75% of the way to the 3800 factor impedance mismatch between air and water

4. Light equations - transparent objects
Fraction light reflected
Fraction light transmitted
Fraction light absorbed
T + A + R = 1 

5. Homework # 2 - Reflection

6. Homework # 2 - Reflection
1a. Reflection at air / cornea
1b. Reflection at aqueous humour / lens
Doesn’t matter which material is 1 and 2

7. #1c. Eye glasses - no eyes Glass Air R1 R2 I0 I2 I1
1st surface reflection
2nd surface reflection
R1 + R2 = = 0.092
Glass
Air R1 R2 I0 I2 I1

8. #1c. Eye glasses - no eyes First surface reflection
If we ignore absorption
I1=(1-R1) * I0 = 0.953I0
Glass
Air R1 R2 I0 I2 I1

9. #1c. Eye glasses - no eyes Glass Air R1 R2 I0 I2 I1
Front surface reflection
If we ignore absorpton
I1=(1-R1) * I0 = 0.953I0
2nd surface reflection
I2 = (1-R2) * I1 = (1-R1)*(1-R2) * I0 = 0.909
So total reflection is Rtot= 1 - I2 = =
R1 + R2 = This is pretty darn close and is a fine answer
Glass
Air R1 R2 I0 I2 I1

10. # 3 - Snell’s law
3a. Refraction at air / cornea
n= n=1.376

11. Homework # 2 - Snell’s law
2a. Refraction at air / cornea
2b. Refraction at aqueous humour / lens
So light bends most at
n= n=1.376
The cornea - 80% of focusing

12. Viewing angles
=24°
Air
cornea
=17°

13. Viewing angles
=24°
Air
cornea
Bends 6.8°
=17°

14. Comparison of bending at cornea and lens
24° ° = 6.8°
Bending at lens
24° ° = 1.3°

15. Homework #4a - photon energy
Energy of photon
350 nm x J / photon
700 nm 2.8 x J / photon
Don’t forget to convert nm to m (109 nm /m)

16. Homework #4b - chemical energy
Energy of one ATP = 7 x J
Energy of photon = NATP (7 x 10-20J/ATP)
350 nm: 5.7 x J = (7 x J/ATP) NATP
NATP = 8 ATP
700 nm: NATP = 4 ATP

17. Homework #5a - photons in a laser
650 nm laser
E (photon) = 3 x J
Laser power = 1 mW = J/s
# photons/s = laser power / photon energy
= J / s / 3 x J
= 3 x 1015 photons / s

18. #5b - absorption Transmission = 1 - Absorption
Transmission = I / I0 = 90%
Absorption = 1 - T - R (ignore reflection)
= = 0.1

19. #5b - absorption Transmission = 1 - Absorption
Transmission = I / I0 = 90%
Absorption = 1 - T - R (ignore reflection)
= = 0.1
# photons absorbed = 0.1 * (# photons from laser)
= 0.1 * (3 x 1015 photons/s * 1s)
= 3 x 1014 photons