SMA Physics

Tag: Waves

  • 10 Multiple Choice Questions on phase difference to path difference conversion formula:

    10 Multiple Choice Questions on phase difference to path difference conversion formula:

    Topic: Wave Optics, Waves

    $$\Delta \phi = \frac{2\pi}{\lambda} \Delta x$$

    Question 1

    What is the correct mathematical relationship between phase difference ($\Delta \phi$) and path difference ($\Delta x$) for a wave of wavelength $\lambda$?

    A) $\Delta \phi = \frac{\lambda}{2\pi} \Delta x$

    B) $\Delta \phi = \frac{2\pi}{\lambda} \Delta x$

    C) $\Delta \phi = 2\pi \lambda \Delta x$

    D) $\Delta \phi = \frac{2\pi \lambda}{\Delta x}$

    • Answer: B

    Question 2

    If the path difference between two interfering light waves is exactly equal to one full wavelength ($\lambda$), what is their phase difference in radians?

    A) $\pi$

    B) $\frac{\pi}{2}$

    C) $2\pi$

    D) $4\pi$

    • Answer: C

    Question 3

    A path difference of $\frac{\lambda}{2}$ corresponds to which of the following phase differences?

    A) $90^\circ$ ($\frac{\pi}{2}$ rad)

    B) $180^\circ$ ($\pi$ rad)

    C) $270^\circ$ ($\frac{3\pi}{2}$ rad)

    D) $360^\circ$ ($2\pi$ rad)

    • Answer: B

    Question 4

    For two points on a traveling wave, the phase difference is found to be $\frac{\pi}{3}\text{ rad}$. If the wavelength of the wave is $60\text{ cm}$, what is the path difference between these two points?

    A) $5\text{ cm}$

    B) $10\text{ cm}$

    C) $20\text{ cm}$

    D) $30\text{ cm}$

    • Answer: B
    • Solution: $\Delta x = \frac{\lambda}{2\pi} \Delta \phi = \frac{60}{2\pi} \times \frac{\pi}{3} = \frac{60}{6} = 10\text{ cm}$.

    Question 5

    In the formula $\Delta \phi = \frac{2\pi}{\lambda} \Delta x$, what does the term $\frac{2\pi}{\lambda}$ physically represent?

    A) Wave velocity ($v$)

    B) Angular frequency ($\omega$)

    C) Propagation constant / Wave number ($k$)

    D) Time period ($T$)

    • Answer: C

    Question 6

    If the path difference between two monochromatic light waves arriving at a point is zero ($\Delta x = 0$), their phase difference will be:

    A) $\pi\text{ rad}$

    B) $2\pi\text{ rad}$

    C) $0\text{ rad}$

    D) Dependent on the wavelength of the light

    • Answer: C

    Question 7

    Two waves having a path difference of $\Delta x = \frac{3\lambda}{4}$ will have a phase difference equal to:

    A) $\frac{\pi}{2}\text{ rad}$

    B) $\pi\text{ rad}$

    C) $\frac{3\pi}{2}\text{ rad}$

    D) $3\pi\text{ rad}$

    • Answer: C

    Question 8

    In a medium where the wavelength of a light wave shrinks to half of its vacuum value ($\lambda’ = \frac{\lambda_0}{2}$), how does the phase difference change for a fixed path difference $\Delta x$?

    A) It becomes half.

    B) It doubles.

    C) It quadruples.

    D) It remains unchanged.

    • Answer: B

    Question 9

    Which of the following conditions for path difference ($\Delta x$) corresponds to a phase difference of $\Delta \phi = 3\pi\text{ rad}$?

    A) $\Delta x = \lambda$

    B) $\Delta x = \frac{3\lambda}{2}$

    C) $\Delta x = 3\lambda$

    D) $\Delta x = \frac{2\lambda}{3}$

    • Answer: B

    Question 10

    Consider the following statements regarding the relation $\Delta \phi = k \Delta x$:

    1. The SI unit of phase difference $\Delta \phi$ is radians.
    2. For a constant path difference, higher frequency waves (shorter wavelengths) will yield a larger phase difference.

    Which of the statements is/are correct?

    A) Only 1

    B) Only 2

    C) Both 1 and 2

    D) Neither 1 nor 2

    • Answer: C