1. A plano-convex lens is placed on a flat glass surface and illuminated with light from below as shown in the diagram below (the angles are exaggerated for clarity). A set of circular fringes is seen by an observer looking straight down. The surface of the convex side of the lens is given by y = bx², where b = 1.00 × 10^-4 cm^-1 and x and y are in centimetres. The light is monochromatic with λ = 579.0 nm.
   (a) Is the centre of the lens dark or bright? Explain.
   (b) What is the linear distance (i.e. Δx) of the m = 3 and m = 4 bright fringes.
   (c) If the lens is 5.00 cm wide, how many bright fringes can be seen in total?
   
   

2. A N-slit grating produces the pattern on a screen 2.00 m distant. A portion of the pattern is shown below (The thick black lines represent maxima and the thin black lines represent secondary maxima). The light source had a wavelength of 555.0 nm.
   (a) What was N (i.e. how many slits are there)? Explain how you can tell.
   (b) What is the spacing of the slits?
   (c) What would the width of the slits be for the rightmost and leftmost maxima in the diagram side to disappear but leave the rest visible?
   
   

3. (a) Two converging are used to make a telescope. The lenses are 92 cm apart and the telescope magnifies objects 200 times. What are the focal lengths of the lenses? Specify which is the objective and which is the eyepiece.
   

   (b) How much energy would a 30 × 10^-12 m photon lose in a collision with a stationary electron, if the photon is scattered at 55°? What would be the velocity of the electron after the collision?

4. A thin layer of oil (t = 500 nm, n_oil = 1.46) is coated on a glass slide (n_glass = 1.80). White light (all wavelengths between 400 nm and 700 nm) shines on the oil from above in diagram (a) and through the oil from below in diagram (b). In each case, determine which wavelengths are enhanced and which are diminished.
   
   

5. In the diagram below, an object of height h = 0.500 cm is placed 30.0 cm to the left of the convex lens.
   (a) Locate the final image.
   (b) Characterize the final image and determine its size.
   (c) Sketch a ray diagram on the diagram.
   
   

6. (a) A beam of aluminum atoms is used to "dope" a semiconductor to give it the proper electrical properties. If the atoms' velocity is required to be (4.5000 ± 0.00001) × 10⁴ m/s, how accurately can the atoms be localized? The mass of a mole of aluminum atoms is 26.98 g and a mole is 6.022 × 10²³.
   

   (b) The tungsten filament in a 100 Watt lightbulb burns at a temperature of 3200 Kelvin. Treating the filament like a blackbody, what is the surface area of the filament? Note that this is an overestimate since not all the 100 W goes into producing light. What is the peak wavelength emitted by the filament?
   

7. (a) Lithium, beryllium, and Mercury have work functions of 2.3 eV, 3.9 eV, and 4.5 eV, respectively. If 400-nm light is incident on each of these metals, determine (i) which metals will release photoelectrons, and (ii) the maximum kinetic energy for the photoelectrons in each case.
   

   (b) Lithium has three protons in its nucleus. If it is ionized to Li++, what is the wavelength of light emitted when its remaining electron undergoes a transition from n = 6 state to n = 2 state?
   

Formulas

Reflection, Refraction, & Polarization:

θi = θr	n = c/v	n1sinθ1 = n2sinθ2
sinθcritical= n2/n1	I = I0cos2θ	tanθp = nlower/nupper

Mirrors & Lenses:

f = ½R	1/o + 1/i = 1/f	1/fcombined = 1/f1 + 1/f2
dapparent = -n2dactual/n1	M = -i/o

Mirrors		Lenses
o	= + object in front of mirror	o	= + object on incident side
o	= - object is behind mirror	o	= - object on transmission side
i	= - image is behind mirror	i	= + image is on transmission side
i	= + image is in front of mirror	i	= - image on incident side side
f,R	= + concave side is mirror	f	= + converging lens, centre is thicker
f,R	= - convex side is mirror	f	= - diverging lens, centre is thin

Optical Instruments:

Msimple = θ/θo = xNP/f	f-number = f/D
Lfilm µ ID2t	MMicroscope = -(L/fobjective)(xNP/feyepiece)
MTelescope = -fobjective/feyepiece

Thin Films

	δreflection = 0	δreflection = π
C.I.	2t/λ' = m	2t/λ' = m + ½	m = 0,1,2,...
D.I.	2t/λ' = m + ½	2t/λ' = m

Interference and Diffraction

C.I.	dsinθ/λ = m	m = 0,1,2,...
D.I.	dsinθ/λ = m + ½

y = mλL/d for small angles	asinθ/λ = m	m = 1,2,3,...
I = 4I0cos(δ/2)sin2(β)/β2	δ = 2πdsinθ/λ	β = πasinθ/λ
αc ≈ 1.22λ/D	R = λ/Δλ = mN

Black Body Radiation

λmax = 2.898 mm-K/T

S = ΣT4

Σ = 5.67 × 10-8 W/K4m2

Photoelectric Effect, X-Rays, and Compton Scattering

c = fλ	E = hf	p = h/λ
KEmax = eV0	KE = hf - φ	λmin = hc/eV
Δλ = λc(1-cosθ)	λc = 2.43 × 10-3 nm	λ = h/mv

Spectral Lines and the Atom

En = -(13.6eV)Z2/n2	ΔxΔp ≥ h / 4π	λ = h/p
p = mv	E = p2/2m

Miscellaneous

visible light : 400 nm ≤ λ ≤ 700 nm	melectron = 9.11 × 10-31 kg
h = 6.626 × 10-34 J-s	1 eV = 1.602 × 10-19 J
hc = 1240 nm-eV	hbar = h/2π
c = 2.998 × 108 m/s

Questions? mike.coombes@kwantlen.ca