Apparent Depth and Total Internal Reflection

📋 Course Outline

1. Real and Apparent Depth
2. Apparent Depth Calculations
3. Apparent Displacement
4. Critical Angle and TIR
5. Critical-Angle Applications

📖 1. Real and Apparent Depth

★ Must-know

📐 Formula — For perpendicular observation at a plane interface, the refractive-index ratio equals the ratio of real depth to apparent depth: $\frac{n_i}{n_r}=\frac{\text{real depth}}{\text{apparent depth}}$.

• The real-depth/apparent-depth relation applies to plane surfaces, requires perpendicular observation, and in the stated simplified form requires the observing eye to be in air.

• When an object in a denser medium is viewed from a rarer medium, its apparent depth is smaller and the virtual image appears closer to the interface; viewing from a denser medium toward a rarer medium gives a larger apparent depth.

Further detail

• A ray from the real object O refracts at the interface and is traced backward by the eye to form a virtual image I at the apparent depth.

📖 2. Apparent Depth Calculations

📐 Formula — When the rarer medium is air, the refractive index of the denser medium satisfies $n=\frac{\text{real depth}}{\text{apparent depth}}$.