Refraction and Snell’s Law: How Light Bends at Boundaries

Why Refraction Happens: Speed Changes at a Boundary

Refraction is the change in direction of light as it crosses from one transparent medium to another (for example, from air into water). The key idea is not “light likes to bend,” but that light changes speed in different media. When part of a wavefront enters a new medium first, that part changes speed first, and the wavefront pivots—so the ray changes direction.

A convenient way to describe “how much a medium slows light” is the refractive index n. Higher n means light travels slower in that material.

• Air: n ≈ 1.00
• Water: n ≈ 1.33
• Common glass: n ≈ 1.5

Bending Toward or Away from the Normal

To talk about bending, we measure angles from the normal, an imaginary line drawn perpendicular to the surface at the point where the ray hits.

• If light goes into a higher index medium (slower): it bends toward the normal (the refracted angle is smaller).
• If light goes into a lower index medium (faster): it bends away from the normal (the refracted angle is larger).

These direction rules let you predict refraction qualitatively before using any equation.

Snell’s Law as a Direction-Prediction Tool

Snell’s law connects the incident angle and refracted angle to the refractive indices:

Continue in our app.

• Listen to the audio with the screen off.
• Earn a certificate upon completion.
• Over 5000 courses for you to explore!

Or continue reading below...

Download the app

n1 sin(θ1) = n2 sin(θ2)

Here:

• n1 = refractive index of the incident medium (where the ray starts)
• n2 = refractive index of the refracted medium (where the ray goes)
• θ1 = angle between incident ray and the normal
• θ2 = angle between refracted ray and the normal

How to Use Snell’s Law Without Getting Computation-Heavy

Even without calculating exact angles, Snell’s law tells you how angles compare:

• If n2 > n1, then sin(θ2) < sin(θ1) so θ2 < θ1 (toward the normal).
• If n2 < n1, then sin(θ2) > sin(θ1) so θ2 > θ1 (away from the normal).

Because sine increases with angle from 0° to 90°, comparing sines is the same as comparing angles in typical refraction situations.

Step-by-Step Problem Pattern (Works for Most Refraction Questions)

Pattern A: Predict the Direction of the Refracted Ray

1. Draw the boundary and the normal. Make the normal clearly perpendicular to the surface at the hit point.

2. Label the incident medium and refracted medium. Ask: “Where is the ray coming from?” and “Where is it going?”

3. Choose n1 and n2 correctly. Use a small reference list (air ~1.00, water ~1.33, glass ~1.5).

4. Use the toward/away rule first. If n increases, bend toward normal; if n decreases, bend away.

5. Check limiting cases.

   • If the ray hits along the normal (θ1 = 0), it should not bend (θ2 = 0).
   • If n1 = n2, it should not bend (same direction).

Pattern B: Compare Angles (No Full Calculation Needed)

Use Snell’s law in comparison form:

sin(θ2) = (n1/n2) sin(θ1)

• If n1/n2 is less than 1, then sin(θ2) is smaller than sin(θ1) → θ2 smaller.
• If n1/n2 is greater than 1, then sin(θ2) is larger than sin(θ1) → θ2 larger (unless you hit a limit—see next section).

Limiting Case: When Refraction Can’t Happen (Critical Angle Idea)

When light tries to go from a higher index medium to a lower index medium (for example, water to air), Snell’s law can demand an impossible value for sin(θ2) (greater than 1). That signals that a refracted ray cannot form for that incident angle.

How to check this without heavy math:

1. Confirm you are going from higher n to lower n (only then can this limit appear).

2. Notice that as θ1 increases, θ2 must increase even more (bending away from the normal).

3. There is a point where the refracted ray would have to skim along the surface (refracted angle 90°). Beyond that, refraction into the second medium cannot occur.

This “skimming” condition is a useful mental checkpoint: if your sketch would require the refracted ray to bend past the surface, something else must happen instead of ordinary refraction.

Hands-On Demonstrations of Refraction

1) The Straw in Water (Apparent Bend)

What you need: clear glass, water, a straw or pencil.

1. Place the straw in the glass and look from the side.
2. Observe that the straw appears “broken” or shifted at the water surface.
3. Move your head up/down and left/right; the apparent bend changes.

What’s happening: Light from the submerged part travels through water then into air. Because it speeds up at the water-to-air boundary (n decreases), rays bend away from the normal. Your brain traces rays back in straight lines, so the underwater portion appears displaced.

Direction check: Water (n≈1.33) → Air (n≈1.00) means bend away from normal, so the apparent position shifts.

2) The Coin That “Rises”

What you need: bowl, coin, water.

1. Put a coin in an empty bowl.
2. Back away until the rim blocks your view of the coin (you can’t see it).
3. Without moving your head, have someone pour water into the bowl.
4. The coin becomes visible again, as if it rose.

What’s happening: With water present, rays from the coin can refract at the water-air surface and reach your eyes even though the straight-line path is blocked. The refracted rays bend away from the normal as they exit water into air, redirecting them upward toward you.

3) Apparent Depth in Pools (Why the Bottom Looks Closer)

When you look into a pool from above, the bottom appears shallower than it really is.

How to reason it out:

• Rays from the bottom travel from water to air and bend away from the normal.
• Your brain assumes light traveled in straight lines through air, so it extends those rays backward into the water.
• Those backward extensions intersect at a point above the real bottom, creating a shallower “apparent” position.

Practical implication: Objects underwater are deeper than they look; this matters for judging depth when reaching or aiming.

Flat Glass Windows: Why Objects Can Shift Sideways (Lateral Displacement)

A flat, parallel-sided glass slab (like a window pane) has two boundaries: air→glass and glass→air. A ray bends toward the normal when entering glass, then bends away from the normal when leaving. Because the surfaces are parallel, the exiting ray ends up parallel to the incoming ray—but not in the same place. It is shifted sideways. This is called lateral displacement.

How to Visualize It Step-by-Step

1. Draw two parallel lines to represent the front and back surfaces of the glass.

2. Draw the normal at the entry point (perpendicular to the surface).

3. Entry (air→glass): since n increases, the ray bends toward the normal inside the glass.

4. Exit (glass→air): since n decreases, the ray bends away from the normal as it leaves.

5. Compare directions: the outgoing ray is parallel to the incoming ray, but it is offset sideways.

What Controls How Big the Shift Is?

• Thickness of the glass: thicker slab → more sideways shift.
• Incident angle: larger angle from the normal → more shift.
• Refractive index: higher n (slower inside) → stronger bending at each surface → more shift.

Everyday Places You Notice Lateral Shift

• Looking at a pencil line through the edge of a thick glass sheet: the line appears displaced.
• Camera filters or protective glass in front of sensors: rays can be laterally shifted, which matters for alignment in precise setups.
• Double-pane windows: multiple slabs can create small but noticeable offsets at oblique viewing angles.

Quick Reference Table: Direction Predictions