Questions: Refraction of Waves

Question 1

A ray of light travels from air (n = 1.0) into a glass block (n = 1.5). What happens to the ray at the boundary?

• A. It speeds up and bends away from the normal, because glass is denser
• B. It slows down and bends toward the normal
• C. It maintains the same speed but changes direction due to a force exerted by the glass surface
• D. It slows down and bends away from the normal

Answer: (B)

Glass has a higher index of refraction (n = 1.5 > 1.0), which means light travels more slowly in glass than in air (n = c/v, so higher n means lower v). When light slows down at a boundary, the wavefront pivots toward the normal — the slower edge gets 'left behind' as the faster portion catches up. Option A reverses both facts: light slows down (doesn't speed up) and bends toward the normal (not away). Option D gets the speed right but the direction wrong — this is the most common misconception. Option C is wrong because refraction is caused by speed change, not by any surface force.

Question 2

What is the correct physical explanation for why a wave changes direction when it crosses a boundary between two media?

• A. The wave is deflected by an electromagnetic force at the boundary between the two materials
• B. The change in wave speed causes the wavefront to pivot — one side of the wavefront reaches the boundary and slows while the other still travels at the original speed
• C. Gravity pulls the wave toward denser media, bending its path
• D. Surface tension at the boundary redirects the wave's momentum

Answer: (B)

Refraction is entirely caused by the difference in wave speed on each side of the boundary — no force is needed. Huygens's principle gives the mechanism: when a wavefront hits the boundary at an angle, the portion that enters the slower medium first is slowed while the portion still in the faster medium continues at full speed. This differential speed causes the wavefront to pivot, changing the direction of propagation. Options A, C, and D all invoke forces or mechanisms that don't exist — refraction is purely a geometric consequence of speed difference.

Question 3

When light exits water (n = 1.33) into air (n = 1.0), it bends toward the normal.

• T. True
• F. False

Answer: False

Light bends *toward* the normal when entering a medium where it slows down (going from lower n to higher n). Exiting water into air means going from higher n to lower n — the light speeds up. When light speeds up at a boundary, the wavefront pivots away from the normal. This is the straw-in-water illusion: light from the submerged portion bends away from the normal as it exits the water, making the straw appear displaced. The rule: toward the normal when slowing, away from the normal when speeding up.

Question 4

The index of refraction n = c/v is always greater than or equal to 1 for any physical medium, because light cannot travel faster in a medium than it does in a vacuum.

• T. True
• F. False

Answer: True

The vacuum speed c = 3 × 10⁸ m/s is the maximum speed at which light can propagate. In any physical medium — glass, water, air, diamond — the interaction of the electromagnetic wave with matter slows the propagation speed, so v ≤ c and therefore n = c/v ≥ 1. Vacuum has n = 1 exactly. Air is approximately 1.0003 (essentially 1). Water is 1.33, glass ranges from 1.5 to 1.9, and diamond is about 2.4. A value of n < 1 would imply faster-than-c propagation, which is not possible for ordinary light in bulk media.

Question 5

Use Huygens's principle to explain why a wavefront bends toward the normal when it enters a medium where the wave travels more slowly.

Model answer: Imagine a straight wavefront — a row of crests — approaching a boundary at an angle. The left edge of the wavefront hits the slower medium first and immediately decelerates, while the right edge is still traveling at full speed in the original medium. Because the two edges are moving at different speeds, the wavefront pivots: the slow left edge falls behind while the fast right edge advances. The direction of wave travel is always perpendicular to the wavefront, so as the wavefront pivots, the direction of propagation rotates toward the normal of the boundary. The greater the speed difference, the more the wavefront pivots, and the more the ray bends.

This Huygens argument is more satisfying than just memorizing 'bends toward the normal when slowing' because it shows *why* — the geometry of a non-uniform wavefront pivot. It also immediately tells you the opposite case: when the wave speeds up, the edge entering the faster medium accelerates first, the wavefront pivots the other way, and the ray bends away from the normal.