Prove, geometrically, that a ray of light entering a plate of glass always emerges in a direction parallel to the incident ray.
Figure the entry refraced ray angle, then do it again for the ray leaving. The start angle should be the same as the leaving angle.
I'm not given an angle though. Do I just make one up?
To prove, geometrically, that a ray of light entering a plate of glass always emerges in a direction parallel to the incident ray, we can use the principles of refraction. Refraction occurs when light passes through a boundary between two different media, such as air and glass.
Here's how we can prove it using a simple geometric approach:
1. Draw a diagram: Start by drawing a horizontal line to represent the boundary between air and the plate of glass. Label this line as "Boundary AB."
2. Incident ray: Now, draw a ray of light coming from air (represented by a line) inclined at an angle to the boundary AB. Label this line as "Incident ray I."
3. Normal line: Construct a line perpendicular to the boundary AB at the point where incident ray I intersects the boundary. This line is called the "Normal line N."
4. Angle of incidence: Measure the angle between the incident ray I and the Normal line N. Label it as "Angle of incidence θ1."
5. Refracted ray: Use a protractor to measure the angle between the Normal line N and the refracted ray R which emerges from the other side of the glass plate. Label it as "Angle of refraction θ2."
6. Observe the result: If the incident ray I is not perpendicular to the boundary AB (θ1 ≠ 90°), it will refract as it enters the glass plate. However, you will notice that the refracted ray R is parallel to the incident ray I if you draw them accurately.
This observation proves that a ray of light entering a plate of glass always emerges in a direction parallel to the incident ray.
Explanation: This phenomenon is due to Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is constant for a given pair of media. In this case, since the light is passing from air to glass, the refractive index of glass is higher than that of air. As a result, the angle of refraction is less than the angle of incidence, but they will still be parallel to each other.
Through this geometric approach and the understanding of Snell's law, you can visually comprehend why a ray of light entering a plate of glass always emerges in a direction parallel to the incident ray.