1. What is nanophotonics? Give an example of a manifestation of nanophotonics.

2. What are free carriers in plasmonic semiconductor nanocrystals?

3. What is the main difference between surface plasmon resonance (SPR) and localized surface plasmon resonance (LSPR)?

please answer ALL THREE questions with detailed answers! please have legible handwrtting if handwritten.

Thank you!!!

A 35-year-old patent clerk needs glasses of 50-cm focal length to read patent applications that he holds 25 cm from his eyes. Five years later, he notices that while wearing the same glasses, he has to hold the patent applications 40 cm from his eyes to see them clearly.

What should be the focal length of new glasses so that he can read again at 25 cm?

Draw band structure diagrams for the following, highlighting on each diagram the valence band, conduction band and the band gap.

(a) Au,

(b) SiO2

(c) intrinsic Ge

(d) p-type Ge

(e) n-type Ge

On each of the band diagrams also indicate the probable location of the Fermi level for (c), (d) and (e) at a temperature of 0 K.

1)An object of mass m = 0.25kg has a horizontal spring attached to its left side, and

slides along a frictionless surface. The spring constant is ? = 0.4 N . At t = 0s, the m

object is displaced 0.1m to the right of its equilibrium position. Its initial velocity is 0.4 m , toward the right.

a) What is the period T of the motion?

b) What is the angular frequency ? ?

c) What is the frequency ? ?

d) What is the total energy E ?

e) What is the amplitude A of the motion? (careful!)

f) What is the phase angle ? ?

g) What is the maximum velocity vmax? (careful!)

h) What is the maximum acceleration amax ?

i) What are the position, velocity, and acceleration at t = ? s?

2)A simple pendulum has a period of 2.40s at a place where g = 9.810 m/s^2 What is the
value of g at another place where this pendulum has a period of 2.41s?

3)A wave travels along a string of linear mass density

Since the floor is rough, it exerts both a normal force N₁ and a frictional force f₁ on the ladder. However, since the wall is frictionless, it exerts only a normal force N₂ on the ladder. The ladder has a length of L = 4.1 m, a weight of W_L = 58.5 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90 kg is standing on the ladder, determine the following.

(a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.)

N1=

N2=

F1=

(b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only.)

N1=

N2=

F1=

Julie throws a ball to her friend Sarah. The ball leaves Julie’s hand a distance 1.0 m above the ground with an initial speed of 10 m/s at an angle 30◦ with respect to the horizontal. Sarah catches the ball 1.0 m above the ground.

(a) What is the horizontal component of the ball’s velocity right before Sarah catches it?

(b) What is the vertical component of the ball’s velocity right before Sarah catches it?

(c) What is the time the ball is in the air?

(d) What is the distance between the two girls?

(e) After catching the ball, Sarah throws it back to Julie. However, Sarah throws it too hard so it is over Julie’s head when it reaches Julie’s horizontal position. Assume the ball leaves Sarah’s hand a distance 1.0 m above the ground, reaches a maximum height of 6 m above the ground, and takes 1.115 sec to get directly over Julie’s head. What is the speed of the ball and the angle with the horizontal when it leaves Sarah’s hand?

(f) How high above the ground will the ball be when it gets to Julie?

A house has well-insulated walls. It contains a volume of 90 m³ of air at 295 K.

(a) Consider heating it at constant pressure. Calculate the energy required to increase the temperature of this diatomic ideal gas by 1.5�C.

(b) If this energy could be used to lift an object of mass m through a height of 2.3 m, what is the value of m?

If a charge "Q" is removed from the inside surface of a hollow sphere of radius "a" with infinite conductivity. (a)How much force is required to remove the charge from the sphere? (b)How much work is done to move the charge to a radius of infinity?

A ball is thrown toward a cliff of height h with a speed of 27m/s and an angle of 60? above horizontal. It lands on the edge of the cliff 3.9slater.

Part AHow high is the cliff?

Part bWhat was the maximum height of the ball?

PartC What is the ball's impact speed?

1) A ball is thrown from the top of a roof at an angle of 20 o with respect to the vertical. 1 s later a ball is dropped from the top of the roof

a) If the height of the roof is 20 m, determine the velocity with which the first ball must be thrown in

order for both balls to land at exactly the same time.

b) Imagine the velocity of the first ball is now known, and instead it is the height of the building which

is unknown. Can you obtain an equation for the height of the building which would result in both balls

landing on the floor at the same time

2. Draw a diagram (concept map) that depicts the relationships between resolution, numerical aperture, refractive index, depth of focus, magnification, working distance, and wavelength. Be sure to indicate whether relationships are positively or inversely related. Note that not all parameters need to have a relationship.

An ideal gas is taken through a complete cycle in three steps: adiabatic expansion with work equal to I25 J, isothermal contraction at 325 K, and increase in pressure at constant volume.

(a) Draw a p-V diagram for the three steps.

(b) How much energy is transferred as heat in step 3, and

(c) is it transferred to or from the gas?

A 0.414 kg object is at rest at the origin of a coordinate system. A 3.17 N force in the positive x direction acts on the object for 2.98 s. What is the velocity at the end of this interval?

b. At the end of this interval, a constant force of 4.04 N is applied in the negative x direction for 4.17 s. What is the velocity at the end of the 4.17 s?

Briefly describe the principle of surface force apparatus

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 44.2 km/s and 57.5 km/s. The slower planet's orbital period is 7.50 years.