Q.A container holds a horizontal layer of turpentine floating on top of water, with air above the turpentine. Turpentine is optically denser than water (it has the larger refractive index), even though it is less dense by mass, which is why it floats; both liquids are optically denser than air. So the refractive indices satisfy $n_{air} < n_{water} < n_{turpentine}$. A ray of light is sent from the air and is incident on the top surface of the turpentine at an oblique angle, then continues down across the turpentine and into the water. Four candidate ray paths are offered, each bending differently at the air-turpentine boundary and at the turpentine-water boundary. Only one path obeys the laws of refraction at both boundaries. Which candidate path is correct?

Concept

Snell's law at each interface: $n_1 \sin\theta_1 = n_2 \sin\theta_2$.

• Going from a rarer to a denser medium ($n_2>n_1$): $\theta_2<\theta_1$, the ray bends toward the normal.
• Going from a denser to a rarer medium ($n_2<n_1$): $\theta_2>\theta_1$, the ray bends away from the normal.

Applying it to the two boundaries

The optical densities are $n_{air} < n_{water} < n_{turpentine}$.

1. Air $\to$ turpentine (rarer $\to$ densest): bends toward the normal.
2. Turpentine $\to$ water (densest $\to$ intermediate): bends away from the normal.

Checking the overall direction …

Method: Applying Snell's Law Across a Stack of Media

When light crosses two or more interfaces in sequence (e.g. air $\to$ liquid A $\to$ liquid B), work one boundary at a time rather than trying to reason about the whole path at once.

Steps

Step 1: Rank the media by refractive index

Write down $n$ for every medium in the order the ray passes through them. This single ranking tells you, at each interface, whether you're going from rarer-to-denser or denser-to-rarer.

Step 2: Apply Snell's law at each interface separately

At each boundary: entering a denser medium ($n_2 > n_1$) bends the ray toward the normal; entering a rarer medium ($n_2 < n_1$) bends it away from the normal. Apply this rule independently at every interface — do not carry over the bend direction from the previous interface.

Step 3: Chain the results and sanity-check the net effect …