Wavelength in Glass: A light beam of frequency 1 × 10^14 Hz enters glass with refractive index n = 1.5. Assuming c = 3 × 10^8 m/s in vacuum, find the wavelength in glass.

Introduction / Context:In a medium of refractive index n, wave speed decreases by a factor n, but frequency remains unchanged across boundaries. Therefore, the wavelength shortens as λ = v/f = (c/n)/f.

Given Data / Assumptions:

• Frequency f = 1 × 10^14 Hz.
• Refractive index n = 1.5.
• c = 3 × 10^8 m/s in vacuum; μr ≈ 1.

Concept / Approach:

Speed in medium: v = c/n. Wavelength in medium: λ = v/f = (c/n)/f. Frequency is invariant at the interface; only speed and wavelength change.

Step-by-Step Solution:

Verification / Alternative check:

Free-space wavelength would be λ0 = c/f = 3 μm; dividing by n = 1.5 gives 2 μm, consistent with the above.

Why Other Options Are Wrong:

• 3 μm: that is λ in vacuum, not in glass.
• 4 μm and 1 μm: inconsistent with λ0/n.
• 0.5 μm: would require n = 6, not 1.5.

Common Pitfalls:

• Changing frequency across boundary (frequency remains constant; wavelength changes).

Final Answer:

2 μm