Section 6.2: Refraction
Refraction is the bending of light as it passes from one medium to another due to a change in speed. The laws of refraction are described by Snell's Law:
- \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \), where \( n \) is the refractive index and \( \theta \) is the angle with the normal.
- The incident ray, refracted ray, and normal lie in the same plane.
- Total internal reflection occurs when light moves from a denser to a rarer medium at an angle greater than the critical angle: \( \theta_c = \arcsin\left(\frac{n_2}{n_1}\right) \) for \( n_1 > n_2 \).
Example: Refraction at a Glass Surface
Light travels from air (\( n_1 = 1.0 \)) into glass (\( n_2 = 1.5 \)) at an incidence angle of 30°. Find the angle of refraction.
Using Snell's Law: \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \) \( 1.0 \cdot \sin 30° = 1.5 \cdot \sin \theta_2 \) \( \sin \theta_2 = \frac{0.5}{1.5} = 0.333 \) \( \theta_2 \approx 19.5° \)
Practice Problems
- Calculate the critical angle for light moving from water (\( n=1.33 \)) to air.
- A ray enters a prism at 40° incidence. The prism refractive index is 1.52. Find the angle of refraction inside the prism.
- Explain why objects appear bent or shifted when viewed through water.
- A light ray passes from glass (\( n=1.5 \)) to air at 45°. Determine if total internal reflection occurs.
- Draw the path of a ray entering a rectangular glass block at an angle and exiting parallel to the incident ray.