Homework Assignment #4 2/24/11

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

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

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

Homework # 2 - Reflection

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

#1c. Eye glasses - no eyes Glass Air R1 R2 I0 I2 I1 1st surface reflection 2nd surface reflection R1 + R2 = 0.046 + 0.046 = 0.092 Glass Air R1 R2 I0 I2 I1

#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

#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 = 1-0.909 = 0.0909 R1 + R2 = 0.092 This is pretty darn close and is a fine answer Glass Air R1 R2 I0 I2 I1

# 3 - Snell’s law 3a. Refraction at air / cornea n=1 n=1.376

Homework # 2 - Snell’s law 2a. Refraction at air / cornea 2b. Refraction at aqueous humour / lens So light bends most at ----- n=1 n=1.376 The cornea - 80% of focusing

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

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

Comparison of bending at cornea and lens 24° - 17.2° = 6.8° Bending at lens 24° - 22.7° = 1.3°

Homework #4a - photon energy Energy of photon 350 nm 5.7 x 10-19 J / photon 700 nm 2.8 x 10-19 J / photon Don’t forget to convert nm to m (109 nm /m)

Homework #4b - chemical energy Energy of one ATP = 7 x 10-20 J Energy of photon = NATP (7 x 10-20J/ATP) 350 nm: 5.7 x 10-19 J = (7 x 10-20 J/ATP) NATP NATP = 8 ATP 700 nm: NATP = 4 ATP

Homework #5a - 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

#5b - absorption Transmission = 1 - Absorption Transmission = I / I0 = 90% Absorption = 1 - T - R (ignore reflection) = 1 - 0.9 = 0.1

#5b - absorption Transmission = 1 - Absorption Transmission = I / I0 = 90% Absorption = 1 - T - R (ignore reflection) = 1 - 0.9 = 0.1 # photons absorbed = 0.1 * (# photons from laser) = 0.1 * (3 x 1015 photons/s * 1s) = 3 x 1014 photons