Step 1 (Formula / Governing Law & Given Data): [0.25 Mark]
The fringe width ($\omega$) in Young's Double Slit Experiment (YDSE) is given by the formula:
$$\omega = \frac{\lambda D}{d}$$Where:
- $\lambda$ = Wavelength of the light used.
- $D$ = Distance between the slits and the screen.
- $d$ = Distance between the two slits.
Since $D$ and $d$ are constant for the experiment, the fringe width is directly proportional to the wavelength: $\omega \propto \lambda$.
Step 2 (Step-by-Step Mathematical Working): [0.5 Mark]
We compare the wavelengths of the three colors used:
- Green light ($\lambda_2$): $\approx 500\text{ nm}$
- Orange light ($\lambda_1$): $\approx 600\text{ nm}$
- Red light ($\lambda_3$): $\approx 700\text{ nm}$
The order of wavelengths is: $\lambda_2 < \lambda_1 < \lambda_3$.
Applying the proportionality $\omega \propto \lambda$:
$$\omega_2 < \omega_1 < \omega_3$$Rearranging this to match the options provided:
$$\omega_3 > \omega_1 > \omega_2$$Step 3 (Final Concluded Answer): [0.25 Mark]
Comparing the derived relation with the given options, the correct choice is (D).
Correct Option: (D) $\omega_3 > \omega_1 > \omega_2$
💡 EL10 Concept Insight:
Think of light waves like ripples in a pond; longer waves (like red) are "stretched out" and create wider gaps between the bright spots on the screen, while shorter waves (like green) are "squashed" and create narrower, tighter fringes.