A ray of light travels from air to water. The refeactive index of water is given by the expression

Analyze the question: A ray goes from air into water. We need the correct expression for the refractive index of water (relative to air).

Concept: Refractive index n for light going from medium 1 (air) to medium 2 (water) can be written in several equivalent ways:

• n = sin i / sin r (angle of incidence over angle of refraction)
• n = velocity in air / velocity in water
• n = wavelength in air / wavelength in water (frequency stays constant, so v = fλ gives the same ratio as the velocities)
• n = real depth / apparent depth

Check each option:

• A. velocity in water / velocity in air. This is inverted. It would be less than 1, but n for water is about 1.33. Wrong.
• B. sin r / sin i. This is also inverted. The correct form is sin i / sin r. Wrong.
• C. apparent depth / real depth. Also inverted. The correct form is real depth / apparent depth. Wrong.
• D. wavelength in air / wavelength in water. Since v = fλ and f does not change when light enters a new medium, n = v_air / v_water = λ_air / λ_water. Correct.

Tip: Remember that refractive index is always bigger than 1 for water. So the "faster" or "larger" quantity (air's speed, air's wavelength, real depth, sin i) goes on top. Options A, B and C each flip one of these, and that is the usual trap in this question.