Condition for sustained interference

In Young's double slit experiment, interference fringes are obtained only when the two waves reaching the screen are of the same frequency (same wavelength) and maintain a fixed phase relation.

What happens here?

• One slit has a red filter $\Rightarrow$ only red light emerges from that slit.
• The other slit has a green filter $\Rightarrow$ only green light emerges from that slit.

Thus, the two slits emit light of different wavelengths: $\lambda_r \neq \lambda_g$

Can red light from one slit interfere with green light from the other slit?

No. Interference requires superposition of waves of the same frequency. Red and green lights have different frequencies, so the cross-term averages out to zero.

Hence, there is no observable interference pattern due to the two slits together.

Checking the options

• A: Alternate red and green fringes — impossible. ❌
• B: Separate interference patterns for red and green — not possible, because for red interference both slits must supply red light, and for green interference both slits must supply green light. Here one slit gives only red and the other only green. ❌
• C: Fringes with green center and red edges — this occurs in white-light YDSE when both slits receive the full white light, not in this filtered case. ❌
• D: No interference fringes — correct. ✅

Final conclusion

Since the two slits transmit different colors, they do not produce mutual interference fringes.

$\boxed{\text{Option D}}$