Physics 2 Lab Final UGA

Exp 12: Reflection and Refraction I

- If angle of incidence exceeds critical angle then there is NO refracted ray and the light suffers Total Internal Reflection

- When angle of incidence (I) = critical (C) angle, angle of refraction is 90deg.

- sin(angleC) = nb/na (na>nb); where na is index of refraction of prism and nb is index of refraction of air

- Optics kit: bench, light source, helium-neon laser, lenses and mirrors

- Procedure:

- place mirror 30cm from edge of table

- pencil 1 15 cm in front of mirror acts as object

- pencil 2 behind mirror; at some position, you can view both image of pencil 1 and direct view of pencil 2 simultaneously

- once the image of 1 and view of 2 line up, measure positions of both pencils w/ respect to mirror and draw ray diagram

Image formation by a plane mirror:

- position of object 15cm and image 13cm

- image is virtual AND erect!

- image is the same size!

- when you move your head side to side, apparent location of the image changes slightly but is mostly similar

Exp 12 (2)

- TIR: semicircular prism and laser to measure angleC and calculate n of prism's material

- laser on left end of bench and screen on the other w/ platform halfway between

- prism on platform and angle of incidence of ray set at ~20deg

- increase angle of I and follow changes in angle of R; angleC will be reached when angle R = 90deg!

Total Internal Reflection:

- critical angle found = 33deg (when angle R = 90deg)

- index of R found by: n(air) x sin(90) = n(prism) x sin(33), where n(air) = 1

- n(prism) = 1.84

- angle of reflection = 33deg (why? angle of refl. = angle of refr. !)

- Does angle of I = angle of R? Yes!

- Why is it important to arrange the prism so that the table's axis passes through midpoint of prism? In regards to Snell's Law, the initial angle would no longer be 90deg, which would disrupt calculation of index of R as we would have to determine the initial angle first.

- Ray diagrams!!

Exp 12 Reflection and Refraction II (3)

Converging Lens:

- rotatable platform on bench near laser end and 20mm block on top, perpendicular to beam

- next, lens w/ focal length 200mm midway along bench

Diverging Lens:

- mount diverging lens (f= -22mm) on bench w/ laser passing through center

- use block to displace beam to one side

Converging Lens:

- Experimental method for finding f:

- To determine experimental f, we set up the lens between the light and screen. We moved the lens towards the screen until the rays converged into one point.

- measured f = 182mm

- nominal f = 200mm

- % error = 9% (remember, (| E - A |/ A) x 100

Diverging Lens:

- Study ray diagram!

- measured: x(1) = 1.2cm; x(2) = 3.6cm; l = 25cm; tan(ang) = 0.096

- calculated f = tan(ang) = x(1) / f => f = x(1) / tan(ang) = 1.2 / 0.096 => f = 131.3mm

- nominal f = 150.0mm

- % error = 12.5%

Exp 13: Image Formation by Lenses

Ideas:

- single thin lenses: 1/p + 1/q =1/f' where p: object distance, q: image distance, -f for diverging lens and +f for converging lens

- M = q/p

Single Converging Lens:

- translucent light diffuser covering light source

- glass slide as object close to light w/ screen at opposite end of bench

- convex (converging) lens f = 200mm on bench to produce real, inverted, reduced image

- position again to produce enlarged image

Two Lenses:

- impossible to obtain real image w/ single diverging lens alone

- move screen 3cm closer to light, mount converging lens for a reduced image

- replace screen and place diverging lens where screen was, move it for a real image

Microscope:

- screen = "initial object"

- f = 127mm lens as "eyepiece" and f = 48mm lens as "objective"

Telescope:

- f = 200mm lens as "objective" and f = 48mm as "eyepiece"

- M = f (objective)/f (eyepiece)

- study ray diagrams!

Single Converging Lens: (reduced)

- when object is outside focal length, a real, inverted, reduced image is formed

- when inside focal length, image is virtual, upright, and englarged

- di = 33cm; hi = 11.8cm; do = 48cm; ho = 12cm

- 1/f' = 1/p + 1/q = 1/48 + 1/33 = 9/176 => f = 176/9 = 19.5cm

- nominal f = 20cm; %error = 2.5%

- measured magnification: M = -hi/ho = -(-11.8cm)/12 = 0.98cm

- calculated magnification: M = q/p = 33/48 = 0.69cm

- % error = 21.8%

(enlarged)

- di = 47cm; hi = 12.3cm; do = 34cm; ho = 12cm

- calculated f = 19.7; % error = 1.4%

- measured M = 1.025cm; calc. M = 1.38cm; % error = 1.08%

Microscope:

- Compared to telescope, the object is much closer and produces an enlarged image rather than reduced

Telescope:

- Our final set up included the lens w/ smaller f a little more than 10cm behind the screen. f(o) > f(e)

Exp 14: Interference and Diffraction I and II

Ideas:

- single-slit diffraction and multiple-slit interference: What are the physical differences? What are the different patterns produced? Why can their patterns occur simultaneously?

Single-Slit:

- Minima: sin(θ) = mλ/a; m = +-1, +-2, ...

- Intensity = Io [sin(β/2)/β/2]^2

- β = 2πa sin(θ)/λ

- slide w/ slits near laser and screen at other bench end

- observing Fresnel diffraction here, but equations are derived from Fraunhofer

- place translator 80cm from slit

- measure light intensity (I) from central max. to 4th min. on one side

Double-Slit: (day 2)

- Maxima: sin(θ) = mλ/d; m = 0, +-1, +-2, ...

Diffraction Grating:

- Maxima: sin(θ) = mλ/d; m = 0, +-1, +-2, ... where d is the slit spacing

- Why is a grating spectrometer a better tool than a double-slit spectrometer?

Single-Slit:

- How does the pattern depend on slit width? The smaller the slit width, the further apart the minima are. The larger the width, the closer the minima are.

- How does pattern for any given slit depend on slit-to-screen distance? As the distance decreases, intensity increases. The pattern becomes more compact as distance decreases.

- angles calculated using sin(θ) = mλ/a; where m = 1 or 2

- How does angle depend on slit width? The angle decreases as the slit width increases.

- 0.08mm wide slit: measured L = 858mm (between slit and fiber optic) using tan(θ) = x/L

- graphed Normalized Intensity vs Position

Double-Slit:

- How does the pattern depend on slit separation? As slit separation increases, the pattern becomes more dense.

- Similarities/differences between single- and double-slit patterns: Single-slit results in a central bright fringe surrounded by alternating dark/bright fringes, while double-slit produces evenly spaced bright fringes. Fringes depend on wavelength.

- The minimum of the single-slit is superimposed w/ the maxima of the double-slit pattern, causing the missing maxima

- 0.08mm wide slits separated by d = 0.250mm: measured distance L = 1315mm (between slit and screen)

Diffraction Grating:

- Measure from central max. to 2nd max. on one side: measured L = 0.435m (between grating and meter stick)

- using tan(θ) = y/L and sin(θ) = mλ/d

- Why is a spectrometer using grating better than one using double-slit? Grating creates a sharper image of the pattern.

Exp 15: Diffraction Grating Spectrometer

Ideas:

- how to operate DGS

- calculate grating spacings and wavelengths from measured spectral lines

- identify unknown substance by its spectrum

- If parallel light of λ is incident normally on a grating, then θ at which intensity (I) of transmitted light is a max. is given by:

- d sin(θ) nλ; where n = 0, 1, 2, ... and d is spacing b/twn slits

- 1/λ = R [1/2^2 - 1/n^2] n = 3, 4, 5... & R (Rydberg constant) = 1.097 x 10^7 m^-1

- 1/λ = R [1/m^2 - 1/n^2]

- various series named after their discoverers have different starting n's, explained by Bohr model

ONLY helium for part 1!

- eyepiece: collimator

- central image = 0 angle ref.

- measure angles of 1st and 2nd order maxima on right and left sides

- calculate d

Rydberg Constant:

- same procedure but calculating R compared to given R

Unknown:

- matching measurements to given wavelengths

Determination of Grating Spacing d:

- measured angles of 1st and 2nd order maxima for red, yellow, blue-green, and violet-blue for the helium spectrum

- averaged right and left maxima angles

- calculated sin(θ)avg then d using d sin(θ) nλ

- measured d(avg) = 1.706 x 10^-6 m

- actual d = 1.667 x 10^-6 m

Rydberg Constant:

- measured angles of 1st and 2nd order maxima (right side) for hydrogen spectrum where Red n = 3, Blue-green n = 4, Purple n = 5, and Dark purple n = 6

- calculated sin(θ), λ(experimental), and R for each color/order

- λ = d sin(θ)/ N where d = 1.667 x 10^-6 m

- 1/λ(exp) = R [1/m^2 - 1/n^2]

- R(avg) = 1.20 x 10^7 (R actual = 1.097 x 10^7)

Unknown:

- scanned over the first order colors visible and wrote down the 5 most prevalent

- ranked each color's brightness

- recorded 1st order maxima on right side of central max.

- calculated sin(θ), λ(experimental), and compared to λ(actual)

- compared our lowest and highest wavelengths as well as amount of spectral lines to the chart of knowns

Exp 16: Electric Fields and Equipotential Lines

Ideas:

- difference b/twn concepts of EF's and electric potential

- draw/identify EF lines and electric equipot. surfaces on diagram

- EF's/EP's behavior near conductors

- electric field: E and force: F on a positive test charge q' is : E = F/q'

- E at a point distance r from point charge q located @ origin of coordinate system is: E = (q/4π εo r^2)r^ where r^ is a unit vector in r direction

- EP is defined by electric potential energy (V) of a point charge at that position: V = q/4π εo r

- electric potential is a scalar quantity while electric field is a vector quantity (magnitude AND direction)

1. a set of lines crossing surface at right angles to direction of E, force moving from + to - (arrows pointing out)

2. a set of surfaces w/ EP = at every point on surface (circles expanding out)

- direction of E is perpendicular to equipot. and magnitude is: E = -ΔV/Δs

Written Procedure:

1) Place the board w/ charges on the bottom of the apparatus

2) Set multimeter to V DC and attach wires to board

3) apparatus sketch

4) With power supply set to 5.81V, place graph paper on top of the charges and plot 5 points where multimeter read at 5V through the wand. Repeat w/ 4V, 3V, 2V, and 1V

5) Draw lines connecting each group of points

6) Repeat with other board

- Map 1. Explain configuration of equipotentials and electric field for 1st set of conductors

- The current flows from positive charge to negative charge. the equipot. lines curve towards both charges on either side. The EF lines extend outward from + charge and travel in a semi-circular pattern where it then meets the - charge. The EF lines have strong curvature near the charges and straighten between the charges.

- Map 2. (Prediction) Explain the drawing:

- The charge will flow from the single + chare to th emultiple - charges aligned on the plate, 1 direct field line and outwardly curved field lines b/c the + charges will repel each other. There is strong curvature of EF lines near the single point charge, then broaden at the plate, and straighten. The equipotential lines always meet these at 90deg.

- Map 2. (Actual) Compare:

- Actual map closely resembles predicted. Our board had scratches resulting in less smooth and consistent equipot. lines, but they still generally followed predicted pattern.

study maps!

Exp 17: Ohm's Law I

Ideas:

- measure whether an electrical device obeys Ohm's Law

- turn a circuit diagram into a working circuit

- Ohm's Law: V = IR

- Series: R(s) = R(1) + R(2); Parallel: 1/R(p) = 1/R(1) + 1/R(2)

- Voltmeter: of very large R; registers V b/twn 2 terminals. Connect in parallel w/ elements for their voltage

- Ammeter: of very low R; registers current through itself. Connect in series w/ element carrying the current you want measured

Part 1: Ohm's Law

1) Connect power supply and 2 resistors; voltmeter in parallel w/ and ammeter in series w/ R(2)

2) Measure current (I in mA) flowing through R(2) as a function of V across R(2). 10 measurements made with voltage ranging from 0-24V

3) Reverse output leads on power supply so current will flow in opposite direction through R(2). Repeat above, recording as negative numbers this time

4) Graph w/ current (I) on y axis and V on x axis

5) Line of best fit and deduce R(2)

- R(2) = 1.08V / 0.016A = 62.5Ω ; R(2) expected = 68Ω

6) Compare deduced R(2) to direct measurement from multimeter: 8.1% error

Ohm's Law for a Diode

1) Replace R(2) w/ diode

2) Repeat above measuring instructions

- recorded currents w/ diode were significantly smaller than R(2) when flowing through 1st direction, and were consistently 0 flowing in opposite direction

3) A smooth curve forms through data points.

Exp 17: Kirchoff's Rules II

Ideas:

- apply Kirchoff's rules to a two-loop electrical circuit containing several resistors and power supplies/batteries

- Kirchoff's Rules: Node Rule, the algebraic sum of ALL currents into a node = 0 and Loop Rule, the algebraic sum of ALL potential differences (V) around any complete circuit loop = 0

- Node: branch point where 3 or more wires come together

- Loop: path through circuit; starts @ one point, passes through 1 or more circuit elements (like V or R), and returns

Part 2: Kirchoff's Rules

1) Construct complex circuit and set 1st power supply V(1) to 12V and 2nd power supply V(2) to 9V

2) Measure 3 currents at each node (N(1) and N(2)) w/ ammeter (that is to be placed in series w/ circuit element studied!) To measure a current, a branch must be broken and ammeter inserted.

- N(1): I(4), I(5), and I(6) => I(5) + I(6) = I(4) which was true!

- N(2): I(1) + I(2) = I(3); proves Node Rule

- We did not need to solved the equations for both as they should be the same (and were!) b/c current leaving battery = current returning to battery

3) Measure voltage drop across R(1), R(2), and R(3) w/ voltmeter (that is to be placed in parallel w/ circuit element studied!)

- ΣV = V(1) - VR(1) - V(2) + VR(2) = 0V; our Σ was 0.21V

- Loop 1 = 0.08V; Loop 2 = 0.13V

4) 3 circuit loops total! Flow from outside to inside; V to R and back to V

Exp 18: Magnetic Field

Ideas:

- measure strength of magnetic field at center of current-carrying coil of wire

- magnetic field (B) at center of single circular turn of current-carrying wire is B = (μo/2a) I ; where a is the radius of the turn of wire and μo is the permeability of free space: μo = 4π x 10^-7 T m/A

- In the case of a coil of N turns of the same radius (a) each carrying same current (I), magnetic field (B) is: B = (μo/2a) NI

Procedure:

- connect 5 turns of coil in series w/ ammeter and power supply. Position coil as far away from DC supply and cords, and so its axis is along N S direction

- turn on power and adjust so current in coil is 1A (needle is not yet deflected b/c B due to coil is in same direction as B due to Earth!)

- turn off power and rotate coil so axis points E W direction

- turn on and see deflection; this configuration has Earth's field and coil's field perpendicular and of unequal mag.

Data Table 1:

- radius of coil = 7.60cm = 0.076m => 2a = 0.152m

- Be (Earth's magnetic field) = 5.0 x 10^-5 T

- μo = 4π x 10^-7 T m/A

- only measured I(1) and had to change from 5 turns to 15 turns at 55deg

- calculated Bc/Be from tan(θ) = Bc/Be using given angles and recorded N as turns (5 or 15)

- calculated NI from turns and recorded I

- calculated B = (μo/2a) NI in T

- after plotting (μo/2a) NI on y-axis and Bc/Be on x-axis, found slope (y2 - y1/x2 - x1) = 4.5 x 10^-5 T w/ 11% error compared to Be !

Data Table 2:

- only measured 3 θ(1) angles and calculated Bc/Be from each angle, with turns (N) being 5, 10, and 15

- same calculations as above

Exp 18 (cont.):

- Angle of deflection is determined by: tan(θ) = Bc/Be; measuring Bc in multiples of Be

- Be = 5.0 x 10^-5 T

- Be = Earth's field

- Bc = Coil's field

- Br = Resultant field and θ = angle of deflection from Be :)

- (Some systematic errors would've been deduced had we'd recorded the currents flowing opposite and taken the average!)

- Data Table 2: Dependence of Bc on number of turns N in coil: using I = 0.50 A and measuring θ when N = 5, 10, and 15

- graph of Bc/Be as a function of (μo/2a) NI

- deduce value of Be from determined slope (calculated Be is due mainly to Earth's field but is strongly influenced by nearby iron and electric currents)

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