Refraction of Light: Lenses — Practice Quiz

A Physics cheat sheet for Refraction of Light: Lenses — every key formula with its symbols defined — plus a medium-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. If the speed of light in a certain material is $2.0 \times 10^8 \text{ m/s}$, and the speed of light in a vacuum is $3.0 \times 10^8 \text{ m/s}$, what is the index of refraction of the material?

    • $1.0$
    • $1.33$
    • $1.5$
    • $2.0$

    Answer: $1.5$

  2. Light passes from air ($n_1 = 1.0$) into glass ($n_2 = 1.5$) with an angle of incidence of $30^\circ$. What is the angle of refraction?

    • $19.5^\circ$
    • $22.0^\circ$
    • $30.0^\circ$
    • $45.0^\circ$

    Answer: $19.5^\circ$

  3. A light ray travels from a medium with an index of refraction $n_1 = 1.6$ into a medium with an index of refraction $n_2 = 1.0$ (air). What is the critical angle for total internal reflection?

    • $30.0^\circ$
    • $38.7^\circ$
    • $41.8^\circ$
    • $45.0^\circ$

    Answer: $38.7^\circ$

  4. An object is placed $20 \text{ cm}$ in front of a converging lens with a focal length of $10 \text{ cm}$. Where will the image be formed?

    • $5 \text{ cm}$
    • $10 \text{ cm}$
    • $15 \text{ cm}$
    • $20 \text{ cm}$

    Answer: $20 \text{ cm}$

  5. An object $5 \text{ cm}$ tall is placed $30 \text{ cm}$ from a lens. If the image is formed $15 \text{ cm}$ on the other side of the lens, what is the magnitude of the image height?

    • $2.5 \text{ cm}$
    • $5.0 \text{ cm}$
    • $7.5 \text{ cm}$
    • $10.0 \text{ cm}$

    Answer: $2.5 \text{ cm}$

  6. A lens has a focal length of $50 \text{ cm}$. What is its refractive power in diopters?

    • $0.5 \text{ D}$
    • $1.0 \text{ D}$
    • $2.0 \text{ D}$
    • $4.0 \text{ D}$

    Answer: $2.0 \text{ D}$

  7. A simple refracting telescope has an objective lens with a focal length of $100 \text{ cm}$ and an eyepiece with a focal length of $5 \text{ cm}$. What is the angular magnification of the telescope?

    • $5$
    • $10$
    • $15$
    • $20$

    Answer: $20$

  8. For total internal reflection to occur, which of the following conditions must be met?

    • Light must travel from a medium with a lower index of refraction to a medium with a higher index of refraction.
    • The angle of incidence must be less than the critical angle.
    • Light must travel from a medium with a higher index of refraction to a medium with a lower index of refraction, and the angle of incidence must be greater than the critical angle.
    • The angle of refraction must be $90^\circ$.

    Answer: Light must travel from a medium with a higher index of refraction to a medium with a lower index of refraction, and the angle of incidence must be greater than the critical angle.

  9. An object is placed $15 \text{ cm}$ from a converging lens with a focal length of $10 \text{ cm}$. If the object is $3 \text{ cm}$ tall, what is the magnitude of the height of the image?

    • $2 \text{ cm}$
    • $3 \text{ cm}$
    • $4.5 \text{ cm}$
    • $6 \text{ cm}$

    Answer: $6 \text{ cm}$

  10. A person needs reading glasses with a power of $2.5 \text{ D}$. What is the focal length of these lenses?

    • $25 \text{ cm}$
    • $40 \text{ cm}$
    • $50 \text{ cm}$
    • $100 \text{ cm}$

    Answer: $40 \text{ cm}$

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