Step-by-Step Guidance for General Physics II Exam Questions

Q1. Graphically find the image location for the lens or mirror shown. Be sure to label the focal point(s) and/or center of curvature.

Background

Topic: Geometric Optics (Ray Diagrams)

This question tests your ability to use ray diagrams to determine the location of an image formed by a lens or mirror, and to properly label key points such as the focal point and center of curvature.

Key Terms and Formulas:

• Focal Point (F): The point where parallel rays converge (for a converging lens/mirror) or appear to diverge from (for a diverging lens/mirror).

• Center of Curvature (C): The center of the sphere from which the mirror/lens surface is taken.

• Principal Axis: The straight line passing through the center of the lens/mirror and its focal point.

• Ray Diagram Rules: For lenses and mirrors, there are standard rays you should draw (e.g., parallel ray, focal ray, center ray).

Step-by-Step Guidance

1. Draw the principal axis and mark the position of the lens or mirror at the origin.

2. Label the focal points (F) on both sides of the lens/mirror, and the center of curvature (C) if it's a mirror.

3. Place the object at the given location and draw at least two rays from the top of the object: (1) a ray parallel to the principal axis, (2) a ray through the focal point, and (3) a ray through the center of curvature (for mirrors).

4. Show how these rays interact with the lens/mirror (e.g., refract, reflect) and where they converge or appear to converge.

Try solving on your own before revealing the answer!

Q2. Old question about capacitors, electric fields and voltage

Background

Topic: Electrostatics (Capacitors)

This question tests your understanding of the relationships between capacitance, electric field, and voltage in a capacitor.

Key Terms and Formulas:

• Capacitance ($C$): $C = \frac{\varepsilon_0 A}{d}$ for a parallel plate capacitor

• Electric Field ($E$): $E = \frac{V}{d}$

• Voltage ($V$): $V = Ed$

• Charge ($Q$): $Q = CV$

Step-by-Step Guidance

1. Identify what quantities are given (e.g., plate area $A$, separation $d$, voltage $V$).

2. Write the symbolic equation for the quantity you are asked to find (e.g., capacitance, electric field).

3. Substitute the given values into the equation, making sure to include units.

4. Check that all units are compatible (e.g., meters, volts, farads).

Try solving on your own before revealing the answer!

Q3. Calculating resistance, conductivity, resistivity, area, length, etc., given enough other information.

Background

Topic: Electric Circuits (Resistivity and Conductivity)

This question tests your ability to use the relationships between resistance, resistivity, conductivity, area, and length.

Key Terms and Formulas:

• Resistance ($R$): $R = \frac{\rho \ell}{A}$

• Resistivity ($\rho$): Material property, units of $\Omega \cdot m$

• Conductivity ($\sigma$): $\sigma = \frac{1}{\rho}$

• Area ($A$): Cross-sectional area, in $m^2$

• Length ($\ell$): Length of the conductor, in $m$

Step-by-Step Guidance

1. Identify which quantities are given and which you need to find.

2. Write the symbolic equation relating the quantities (e.g., $R = \frac{\rho \ell}{A}$).

3. Substitute the known values into the equation, including units.

4. Check that all units are compatible and convert if necessary.

Try solving on your own before revealing the answer!

Q4. Electric force concepts: Charge vs number of charges; flavor of charges from given information (multiple-choice)

Background

Topic: Electrostatics (Coulomb's Law and Charge Quantization)

This question tests your understanding of the relationship between the amount of charge and the number of elementary charges, as well as the nature (positive/negative) of charges.

Key Terms and Formulas:

• Elementary Charge ($e$): $e = 1.602 \times 10^{-19} \text{ C}$

• Total Charge ($Q$): $Q = n \cdot e$ where $n$ is the number of charges

• Coulomb's Law: $F = \frac{k |q_1 q_2|}{r^2}$

Step-by-Step Guidance

1. Identify whether the question is asking about total charge or number of charges.

2. Use the relationship $Q = n \cdot e$ to convert between total charge and number of charges.

3. For force questions, use Coulomb's Law to relate the charges and the force.

4. Consider the sign of the charges to determine the direction of the force (attractive or repulsive).

Try solving on your own before revealing the answer!

Q5. Electric potential concepts with numbers.

Background

Topic: Electric Potential (Voltage)

This question tests your ability to calculate electric potential given charge, distance, and other relevant quantities.

Key Terms and Formulas:

• Electric Potential ($V$): $V = \frac{kQ}{r}$

• Potential Difference ($\Delta V$): $\Delta V = V_2 - V_1$

• Work ($W$): $W = q \Delta V$

Step-by-Step Guidance

1. Identify the given values (e.g., charge $Q$, distance $r$).

2. Write the symbolic equation for electric potential.

3. Substitute the known values into the equation, including units.

4. Check that all units are compatible (e.g., meters, coulombs, volts).

Try solving on your own before revealing the answer!

Q6. A thin lens is situated at the origin. The lens is to have a focal length of [f]cm and be made out of [material] (n=[n]). The object of interest OR its image is [x]cm to the [direction] of the lens and is [y]cm tall.

Background

Topic: Lens Maker's Formula and Image Formation

This question tests your ability to use the lens maker's formula and the thin lens equation to find radii, focal length, or image location.

Key Terms and Formulas:

• Lens Maker's Formula: $\frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$

• Thin Lens Equation: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$

• Magnification: $m = \frac{h_i}{h_o} = -\frac{d_i}{d_o}$

Step-by-Step Guidance

1. Identify the given values: focal length $f$, index of refraction $n$, object distance $d_o$, object height $h_o$.

2. For radii, use the lens maker's formula and solve for $R_1$ and $R_2$ (if both are equal, $R_1 = -R_2$).

3. For image location, use the thin lens equation to solve for $d_i$.

4. For image height, use the magnification formula.

Try solving on your own before revealing the answer!

Q7. Use the circuit below for this question. A resistor circuit is connected to a coil with [n] turns and area [A]m2. Assume the current rises linearly from zero to the maximum current in [t]ms (a major simplification). At this maximum current, the magnetic field created by the coil is [B]mT. The coil has resistance [R] as shown in the figure.

Background

Topic: Electromagnetic Induction and Circuits

This question tests your ability to calculate resistance, current, magnetic flux, and induced emf in a coil.

Key Terms and Formulas:

• Ohm's Law: $I = \frac{V}{R}$

• Magnetic Flux ($\Phi$): $\Phi = B \cdot A \cdot n$

• Faraday's Law: $\text{emf} = -\frac{\Delta \Phi}{\Delta t}$

Step-by-Step Guidance

1. Calculate the equivalent resistance of the circuit using the given values.

2. Use Ohm's Law to find the maximum current: $I = \frac{V}{R}$.

3. Calculate the change in magnetic flux: $\Delta \Phi = n \cdot (B_{max} \cdot A - 0)$.

4. Use Faraday's Law to find the average induced emf: $\text{emf} = -\frac{\Delta \Phi}{\Delta t}$.

Try solving on your own before revealing the answer!

Q8. Thin films similar to a class example.

Background

Topic: Thin Film Interference

This question tests your ability to analyze constructive and destructive interference in thin films.

Key Terms and Formulas:

• Condition for constructive interference: $2 t = m \lambda / n$ (with phase shift consideration)

• Condition for destructive interference: $2 t = (m + 1/2) \lambda / n$

• Phase shift: Occurs when light reflects off a medium with higher refractive index.

Step-by-Step Guidance

1. Identify the thickness $t$, wavelength $\lambda$, and refractive index $n$ of the film.

2. Determine whether there is a phase shift upon reflection.

3. Write the condition for constructive or destructive interference, depending on the question.

4. Substitute the known values into the formula.

Try solving on your own before revealing the answer!

Q9. Write the complete sinusoidal electric field equation using both COS and SIN for a traveling EM wave in the [?] direction, with amplitude [Emax], period [T] and wavelength [λ] and ϕ=0. Explain how you set the signs.

Background

Topic: Electromagnetic Waves

This question tests your ability to write the mathematical expression for a traveling electromagnetic wave.

Key Terms and Formulas:

• General form: $E(x, t) = E_{max} \cos(kx - \omega t + \phi)$ or $E(x, t) = E_{max} \sin(kx - \omega t + \phi)$

• Wave number: $k = \frac{2\pi}{\lambda}$

• Angular frequency: $\omega = \frac{2\pi}{T}$

• Phase constant: $\phi$ (here, $\phi = 0$)

Step-by-Step Guidance

1. Write the general equation for the electric field of a traveling wave.

2. Substitute the given amplitude, period, and wavelength into the expressions for $k$ and $\omega$.

3. Set $\phi = 0$ as specified.

4. Explain the sign convention: If the wave travels in the positive x-direction, use $(kx - \omega t)$; for negative x-direction, use $(kx + \omega t)$.

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Q10. Snell’s law question which requires understanding of the visible consequences of TIR.

Background

Topic: Refraction and Total Internal Reflection (TIR)

This question tests your ability to apply Snell's law and understand when TIR occurs and its consequences.

Key Terms and Formulas:

• Snell's Law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$

• Critical Angle: $\theta_c = \sin^{-1} \left( \frac{n_2}{n_1} \right)$ (for $n_1 > n_2$)

• Total Internal Reflection: Occurs when $\theta_1 > \theta_c$ and light cannot exit the medium.

Step-by-Step Guidance

1. Identify the indices of refraction for both materials ($n_1$, $n_2$).

2. Use Snell's law to relate the angles of incidence and refraction.

3. Calculate the critical angle using the formula above.

4. Discuss the visible consequences when the angle of incidence exceeds the critical angle (e.g., TIR, no refracted ray).

Try solving on your own before revealing the answer!