8. a light beam enters a piece of window glass (n=1.47) at an incidence angle of 59. Find the angle it makes to the normal as it exists from the other side of the flat window glass. What general rule can you conclude?
I would consider Snell's law.
To solve this problem, we can use the law of refraction, also known as Snell's law. The law of refraction states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two different media:
n1 * sin(θ1) = n2 * sin(θ2)
where:
- n1 and n2 are the indices of refraction of the two media
- θ1 is the angle of incidence
- θ2 is the angle of refraction
In this case, the incident medium is air (with an index of refraction of approximately 1), and the refractive medium is the window glass (with an index of refraction of 1.47). The given angle of incidence is 59 degrees.
Let's first find the angle of refraction using Snell's law:
1 * sin(59) = 1.47 * sin(θ2)
Now, solve for θ2 by dividing both sides of the equation by 1.47:
sin(θ2) = (1 * sin(59)) / 1.47
θ2 = arcsin((1 * sin(59)) / 1.47)
Using a calculator, you can find that θ2 is approximately 39.5 degrees. Therefore, the angle the light beam makes to the normal as it exits from the other side of the flat window glass is approximately 39.5 degrees.
From this problem, we can conclude the general rule that when light passes from air to a denser medium (e.g., glass), the angle of refraction (angle with respect to the normal) is smaller than the angle of incidence, and vice versa. This is known as the rule of refraction or Snell's law.