Step 1: Effect of Plate
Introducing a glass plate shifts the entire fringe pattern.
Step 2: Fringe Width Independence
Fringe width $\beta = \lambda D / d$ depends on wavelength, slit separation, and screen distance.
Step 3: Conclusion
Since these parameters do not change when the plate is added, the fringe width remains unchanged at 0.3 mm.
Final Answer: (b)