The whole interference setup enters a liquid

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Problem: The whole interference setup enters a liquid
A fixed double-slit setup has fringe spacing 3 mm in air. It is immersed in a uniform medium of refractive index 1.50; geometry and light frequency stay fixed.
Question: Find its new fringe spacing.
Givens:
- βair = 0.003 m
- n = 1.50
Assumptions: Coherent double slit, unchanged geometry and source frequency; uniform nondispersive medium of index 1.50; paraxial far field.
Choices (LaTeX):
A. 4.5\ \mathrm{mm}
B. 3\ \mathrm{mm}
C. 1.333\ \mathrm{mm}
D. 2\ \mathrm{mm}

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.