what is the general trend of the critical angle as the refractive index increases?
http://www.physicsclassroom.com/class/refrn/Lesson-3/The-Critical-Angle
nr must be smaller than ni because there is no such thing as a sine with a value greater than one. As nr increases closer to n incident the critical angle gets closer to 90 degrees (sin 90 = 1.00) In other words as nr increases to close to ni, the incoming ray can be just about parallel to the interface and still pass through, just about parallel to the interface on the other side.
The critical angle is the angle of incidence at which light traveling from a medium with a higher refractive index to a medium with a lower refractive index is totally internally reflected. The general trend of the critical angle as the refractive index increases can be summarized as follows:
1. As the refractive index increases, the critical angle decreases.
2. In other words, as the refractive index of the medium through which the light is passing increases, the angle at which total internal reflection occurs becomes smaller.
This trend can be explained by Snell's Law, which states that the angle of incidence is inversely proportional to the refractive indices of the two media. As the refractive index of the medium through which the light is passing increases, the angle of incidence required for total internal reflection becomes smaller.
The critical angle is an important concept in optics and is closely related to the refractive index of a medium. To understand the general trend of the critical angle as the refractive index increases, we need to understand the relationship between these two quantities.
The critical angle is defined as the angle of incidence at which light, traveling from a medium of higher refractive index to a medium of lower refractive index, undergoes total internal reflection. It occurs when the angle of refraction becomes 90 degrees.
Now, let's consider Snell's Law, which describes the relationship between the angles of incidence and refraction:
n1 * sin(theta1) = n2 * sin(theta2)
In this equation, n1 and n2 represent the refractive indices of the two media, and theta1 and theta2 are the angles of incidence and refraction, respectively. The refractive index is a measure of how much slower light travels through a medium compared to a vacuum.
To determine the critical angle, we need to find the angle of incidence for which the angle of refraction becomes 90 degrees. Mathematically, this can be written as:
90 degrees = arcsin(n2 / n1)
Here, n1 is the refractive index of the medium light is coming from (higher refractive index), and n2 is the refractive index of the medium light is entering (lower refractive index).
Now, as the refractive index increases, the critical angle also increases. This can be understood by observing the equation for the critical angle. The critical angle is inversely proportional to the refractive index. So, as the refractive index of the medium increases, the critical angle also increases.
In simple terms, higher refractive index materials tend to bend light more, resulting in a larger critical angle for total internal reflection to occur.
To summarize, the general trend of the critical angle as the refractive index increases is that the critical angle also increases.