Refraction of Light: Lenses — Hard Practice Quiz

A Physics cheat sheet for Refraction of Light: Lenses — every key formula with its symbols defined — plus a hard-level practice quiz to test recall.

Formulas & key concepts

Index of Refraction: Ratio of speed of light in vacuum \(c\) to speed in material \(v\).

$$n = \frac{c}{v}$$

Snell's Law: Relates indices of refraction \(n\) and angles \(\theta\) for light crossing an interface.

$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$

Critical Angle: Angle of incidence \(\theta_c\) for total internal reflection (where \(n_1 > n_2\)).

$$\sin \theta_c = \frac{n_2}{n_1}$$

Thin Lens Equation: Relates object distance \(d_o\), image distance \(d_i\), and focal length \(f\).

$$\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f}$$

Magnification Equation: Relates magnification \(m\), image height \(h_i\), object height \(h_o\), and distances.

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

Lens Power: Refractive power \(P\) in diopters (D) is the inverse of focal length \(f\) in meters.

$$P = \frac{1}{f}$$

Telescope Magnification: Angular magnification \(M\) of a telescope with objective \(f_o\) and eyepiece \(f_e\).

$$M \approx -\frac{f_o}{f_e}$$

Practice quiz

  1. A light ray travels from a medium with index of refraction $n_A$ into a medium with index $n_B$. The speed of light in medium A is $v_A = 2.0 \times 10^8 \text{ m/s}$, and in medium B it is $v_B = 2.5 \times 10^8 \text{ m/s}$. What is the angle of refraction $\theta_B$ when light travels from medium A to medium B at an angle of incidence $\theta_A$ equal to half the critical angle for total internal reflection from medium A to medium B? (Assume speed of light in vacuum $c = 3.0 \times 10^8 \text{ m/s}$).

    • $34.0^\circ$
    • $26.6^\circ$
    • $41.8^\circ$
    • $53.1^\circ$

    Answer: $34.0^\circ$

  2. A converging lens has a power of $5.0 \text{ D}$. An object of height $2.0 \text{ cm}$ is placed $30 \text{ cm}$ in front of the lens. What is the height of the image formed, and is it real or virtual?

    • $4.0 \text{ cm}$, real
    • $4.0 \text{ cm}$, virtual
    • $1.3 \text{ cm}$, real
    • $1.3 \text{ cm}$, virtual

    Answer: $4.0 \text{ cm}$, real

  3. An object is placed at a distance $d_o$ from a converging lens with focal length $f$. If the object is moved to a new position $d_o' = 2f$, how does the absolute magnification $|m|$ change compared to when $d_o = 3f$?

    • It doubles.
    • It halves.
    • It quadruples.
    • It remains the same.

    Answer: It doubles.

  4. Light travels from medium 1 to medium 2. If the critical angle for total internal reflection from medium 1 to medium 2 is $\theta_c$, what is the angle of incidence $\theta_1$ in medium 1 such that the angle of refraction $\theta_2$ in medium 2 is $\theta_c$? Express $\sin \theta_1$ in terms of $\theta_c$.

    • $\sin \theta_1 = \sin^2 \theta_c$
    • $\sin \theta_1 = \sin \theta_c$
    • $\sin \theta_1 = \frac{1}{\sin \theta_c}$
    • $\sin \theta_1 = \frac{\sin \theta_c}{2}$

    Answer: $\sin \theta_1 = \sin^2 \theta_c$

  5. A light ray passes from medium A to medium B, then from medium B to medium C. The speed of light in medium A is $v_A$, in medium B is $v_B$, and in medium C is $v_C$. If $v_A > v_B > v_C$, and the angle of incidence at the A-B interface is $\theta_{AB}$, which of the following statements is true regarding the angle of refraction $\theta_{BC}$ at the B-C interface, assuming light enters B from A at $\theta_{AB}$ and then enters C from B?

    • $\theta_{BC} < \theta_{AB}$
    • $\theta_{BC} = \theta_{AB}$
    • $\theta_{BC} > \theta_{AB}$
    • The relationship depends on the specific values of $v_A, v_B, v_C$.

    Answer: $\theta_{BC} < \theta_{AB}$

  6. A two-lens system consists of a converging lens $L_1$ with power $P_1$ and a diverging lens $L_2$ with power $P_2$. An object is placed at a distance $d_o$ from $L_1$. The lenses are separated by a distance $D$. If the final image formed by the system is virtual and upright, what can be inferred about the relative positions and types of images formed by $L_1$ and $L_2$?

    • $L_1$ forms a real, inverted image, which acts as a real object for $L_2$.
    • $L_1$ forms a virtual, upright image, which acts as a real object for $L_2$.
    • $L_1$ forms a real, inverted image, which acts as a virtual object for $L_2$.
    • $L_1$ forms a virtual, upright image, which acts as a virtual object for $L_2$.

    Answer: $L_1$ forms a real, inverted image, which acts as a virtual object for $L_2$.

  7. A refracting telescope is constructed using an objective lens with power $P_o$ and an eyepiece lens with power $P_e$. If the angular magnification of the telescope is $M$, and the focal length of the objective is doubled while the focal length of the eyepiece is halved, what is the new angular magnification $M'$ in terms of $M$?

    • $M' = M/4$
    • $M' = M/2$
    • $M' = 2M$
    • $M' = 4M$

    Answer: $M' = 4M$

  8. Light travels from medium 1 to medium 2. The ratio of the speed of light in medium 1 to medium 2 is $v_1/v_2 = 1.25$. If light is incident from medium 1 to medium 2 at an angle $\theta_1 = 30^\circ$, what is the ratio of $\sin \theta_2$ to the sine of the critical angle $\sin \theta_c$ for total internal reflection from medium 2 to medium 1?

    • $0.4$
    • $0.5$
    • $0.625$
    • $0.8$

    Answer: $0.5$

  9. An object is placed at a distance $d_o$ from a converging lens. The image formed has a magnification $m$. If the object is moved to a new position such that the new image distance is $d_i' = 2d_i$, where $d_i$ is the original image distance, what is the new magnification $m'$ in terms of the original magnification $m$ and the focal length $f$?

    • $m' = 2m$
    • $m' = 2m - 1$
    • $m' = m^2$
    • $m' = (m-1)/2$

    Answer: $m' = 2m - 1$

  10. A compound microscope uses an objective lens with power $P_o = 50 \text{ D}$ and an eyepiece lens with power $P_e = 20 \text{ D}$. The lenses are separated by a distance of $25 \text{ cm}$. An object is placed $2.1 \text{ cm}$ in front of the objective lens. What is the total magnification of the microscope?

    • $20$
    • $4.55$
    • $100$
    • $200$

    Answer: $4.55$

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