Interference and Wave Nature of Light — Practice Quiz

A Physics cheat sheet for Interference and Wave Nature of Light — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Formulas & key concepts

Young's Double Slit (Bright Fringes): Angle \(\theta\) for constructive interference (bright fringes) with slit separation \(d\).

$$\sin \theta = m \frac{\lambda}{d}$$

Where: \(m = 0, 1, 2, \dots\)

Young's Double Slit (Dark Fringes): Angle \(\theta\) for destructive interference (dark fringes) with slit separation \(d\).

$$\sin \theta = (m + \frac{1}{2}) \frac{\lambda}{d}$$

Where: \(m = 0, 1, 2, \dots\)

Single Slit Diffraction (Dark Fringes): Angle \(\theta\) for destructive interference (dark fringes) with slit width \(W\).

$$\sin \theta = m \frac{\lambda}{W}$$

Where: \(m = 1, 2, 3, \dots\) (Note: \(m \neq 0\))

Resolving Power (Rayleigh Criterion): Minimum angular separation \(\theta_{min}\) (in radians) to resolve two point sources with aperture diameter \(D\).

$$\theta_{min} \approx 1.22 \frac{\lambda}{D}$$

Diffraction Grating (Principal Maxima): Angle \(\theta\) for principal maxima with slit separation \(d\).

$$\sin \theta = m \frac{\lambda}{d}$$

Where: \(m = 0, 1, 2, \dots\)

Practice quiz

  1. A double-slit experiment uses light of wavelength $500 \text{ nm}$. The slits are separated by $0.1 \text{ mm}$. What is the angular position of the first-order bright fringe?

    • $0.005 \text{ rad}$
    • $0.010 \text{ rad}$
    • $0.0025 \text{ rad}$
    • $0.0075 \text{ rad}$

    Answer: $0.005 \text{ rad}$

  2. In a Young's double-slit experiment, light with a wavelength of $600 \text{ nm}$ passes through slits separated by $0.2 \text{ mm}$. What is the angular position of the first-order dark fringe ($m=0$ for the first dark fringe after the central bright fringe)?

    • $0.0015 \text{ rad}$
    • $0.0030 \text{ rad}$
    • $0.00075 \text{ rad}$
    • $0.0020 \text{ rad}$

    Answer: $0.0015 \text{ rad}$

  3. Monochromatic light of wavelength $550 \text{ nm}$ is incident on a single slit of width $0.05 \text{ mm}$. What is the angular position of the first minimum (dark fringe)?

    • $0.011 \text{ rad}$
    • $0.0055 \text{ rad}$
    • $0.022 \text{ rad}$
    • $0.008 \text{ rad}$

    Answer: $0.011 \text{ rad}$

  4. A telescope has an objective lens with a diameter of $10 \text{ cm}$. If it observes light with an average wavelength of $550 \text{ nm}$, what is the minimum angular separation (in radians) it can resolve according to the Rayleigh criterion?

    • $6.71 \times 10^{-6} \text{ rad}$
    • $5.50 \times 10^{-6} \text{ rad}$
    • $1.22 \times 10^{-5} \text{ rad}$
    • $1.10 \times 10^{-5} \text{ rad}$

    Answer: $6.71 \times 10^{-6} \text{ rad}$

  5. A diffraction grating has $5000$ lines per centimeter. When light of wavelength $600 \text{ nm}$ is incident normally on the grating, what is the angular position of the first-order principal maximum?

    • $17.46^\circ$
    • $30.00^\circ$
    • $11.54^\circ$
    • $23.58^\circ$

    Answer: $17.46^\circ$

  6. Which of the following formulas correctly describes the angular positions of bright fringes in a Young's double-slit experiment?

    • $\sin \theta = m \frac{\lambda}{d}$
    • $\sin \theta = (m + \frac{1}{2}) \frac{\lambda}{d}$
    • $\sin \theta = m \frac{\lambda}{W}$
    • $\theta_{min} \approx 1.22 \frac{\lambda}{D}$

    Answer: $\sin \theta = m \frac{\lambda}{d}$

  7. The formula $\sin \theta = m \frac{\lambda}{W}$ (for $m = 1, 2, 3, \dots$) describes the angular positions of:

    • Bright fringes in a double-slit experiment.
    • Dark fringes in a double-slit experiment.
    • Dark fringes in a single-slit diffraction experiment.
    • Principal maxima in a diffraction grating.

    Answer: Dark fringes in a single-slit diffraction experiment.

  8. In a Young's double-slit experiment, if the wavelength of light is increased, what happens to the angular separation between adjacent bright fringes?

    • It increases.
    • It decreases.
    • It remains the same.
    • It depends on the slit separation.

    Answer: It increases.

  9. To improve the resolving power of a telescope (i.e., decrease $\theta_{min}$), which of the following modifications would be most effective?

    • Using light with a longer wavelength.
    • Decreasing the diameter of the objective lens.
    • Using light with a shorter wavelength.
    • Increasing the distance to the observed objects.

    Answer: Using light with a shorter wavelength.

  10. Which of the following phenomena uses the same mathematical formula for its principal maxima as Young's double-slit experiment uses for its bright fringes?

    • Single-slit diffraction dark fringes.
    • Young's double-slit dark fringes.
    • Diffraction grating principal maxima.
    • Rayleigh criterion for resolving power.

    Answer: Diffraction grating principal maxima.

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