Laser Refraction

About

When a beam of light crosses the boundary between two transparent media — such as air and water — it changes direction. This bending is governed by Snell's Law: n₁ sin θ₁ = n₂ sin θ₂, where n₁ and n₂ are the indices of refraction of the two media, and θ₁, θ₂ are the angles of the beam measured from the normal to the surface. This simulation lets you drag a laser pen around a circular water tank and observe refraction in real time, with live angle readouts so you can verify the law numerically.

When light travels from a denser medium into a less dense one (water into air), Snell's Law predicts that the refracted angle grows faster than the incident angle. At a specific angle — the critical angle (≈ 48.6° for water) — the refracted ray would emerge at 90°, grazing the surface. Beyond the critical angle, no transmitted ray is possible; all the light reflects back into the denser medium. This is Total Internal Reflection (TIR), the principle behind optical fibres, diamond brilliance, and prismatic periscopes.

Even below the critical angle, some light is reflected at every interface. The Fresnel equations (Rs and Rp for the two polarisation components) quantify this partial reflection. As the incident angle approaches the critical angle from below, the reflected fraction climbs steeply toward 100%, and the transmitted beam visibly dims — an effect you can observe by slowly rotating the laser pen from inside the water half.

Learning Goals

• Apply Snell's Law (n₁ sin θ₁ = n₂ sin θ₂) to predict the direction of a refracted beam and verify the prediction against the live readout.
• Determine the critical angle experimentally by rotating the laser until TIR occurs, then verify it matches the formula θ_c = arcsin(n₂/n₁).
• Explain why Total Internal Reflection only occurs when light travels from a denser medium (water, n = 1.33) into a less dense medium (air, n = 1.00).
• Observe how partial Fresnel reflection increases as the incident angle approaches the critical angle, causing the transmitted beam to fade before TIR is reached.
• Distinguish between the angle of incidence, angle of refraction, and angle of reflection, and identify each in the diagram while the laser pen is dragged.

How to Use

• Drag the laser pen — click or tap the metallic pen body on the rim of the tank and drag it around the circle. The beam updates instantly as you move.
• Observe refraction — with the laser in the top half (air), watch the beam bend toward the normal as it enters the water. Check the readout to compare θ₁ and θ₂.
• Cross the boundary — drag the pen into the bottom half (water) to observe the water→air case. The beam now bends away from the normal and a faint reflected beam appears.
• Find Total Internal Reflection — slowly increase the angle (move pen toward horizontal) from the water side until the refracted beam disappears and only the reflected beam remains. The readout will show "Total internal reflection".
• Use the slider — the angle slider below the title provides fine-grained control for landing precisely on specific angles (e.g., exactly 30° or 48.6° critical angle).