Young's Double Slit Fringe Separation: Screen Distance vs Wavelength

This question requires analyzing two statements about fringe separation in Young's double-slit experiment (YDS), considering the effect of screen distance and wavelength.

Analyzing Statement I: Screen Distance Effect

Statement I suggests that the angular separation of fringes increases as the screen is moved away from the slits.

In YDS, the angular separation ($\theta$) of fringes is defined by:

$ \theta \approx \frac{\lambda}{d} $

Here, $\lambda$ represents the wavelength of light, and $d$ is the separation between the slits.

Crucially, this formula shows that the angular separation ($\theta$) depends solely on the wavelength and the slit separation, not on the distance ($D$) between the slits and the screen.

Increasing the distance $D$ increases the *linear* fringe width ($\beta = \frac{\lambda D}{d}$) but leaves the *angular* separation ($\theta$) unchanged.

Conclusion: Statement I is false.

Analyzing Statement II: Wavelength Effect

Statement II proposes that the angular separation increases when a higher wavelength monochromatic source replaces the original one.

From the formula $\theta \approx \frac{\lambda}{d}$, it's clear that the angular separation ($\theta$) is directly proportional to the wavelength ($\lambda$).

If the wavelength ($\lambda$) increases, and the slit separation ($d$) remains constant, the angular separation ($\theta$) must also increase.

Conclusion: Statement II is true.

Determining the Correct Option

Summarizing the findings:

• Statement I: False
• Statement II: True

Therefore, the correct option is the one stating that Statement I is false and Statement II is true.