# Finding critical angles and index of refractions

• mark9159
In summary, the conversation discusses how to find the critical angle and index of refraction for a material with an index of refraction of 1.75 and cubic zirconium with a critical angle of 29.2º. It is explained that the critical angle can be found using the formula sin(critical angle) = 1/n, with n being the index of refraction. The index of refraction can be found by using the formula n = 1/sin(critical angle). The conversation also includes a tip for setting the TI-83 Plus calculator into degree mode.
mark9159
im having trouble setting my TI-83 Plus into "degree mode" so i can't seem to get the answers for these problems...im probably doing them wrong too

A material has an index of refraction of 1.75. What is the critical angle for this material?

Sin(critical angle)=1/n, n being the index of refraction
how would i set up the formula? (critical angle)= Sin(n) ?? I am so confused

and

The critical angle for cubic zirconium is 29.2º. What is the index of refraction?

so...Sin(29.2º)= 1/n?...

my answer for this question is 2.049, rounded to 2.05

thank you,

mark

mark9159 said:
im having trouble setting my TI-83 Plus into "degree mode" so i can't seem to get the answers for these problems...im probably doing them wrong too

A material has an index of refraction of 1.75. What is the critical angle for this material?

Sin(critical angle)=1/n, n being the index of refraction
how would i set up the formula? (critical angle)= Sin(n) ?? I am so confused

and

The critical angle for cubic zirconium is 29.2º. What is the index of refraction?

so...Sin(29.2º)= 1/n?...

my answer for this question is 2.049, rounded to 2.05

thank you,

mark
In the following discussion, sin-1 is the Inverse Sine function.
SOLUTION HINTS:
a) sin(θcrit) = (1/n) :: ⇒ :: θcrit = sin-1(1/n) = sin-1{1/(1.75)} = (34.85 deg)
b) sin(29.2 deg) = 1/n :: ⇒ :: n = 1/{sin(29.2 deg)] = (2.05)

~~

Last edited:
mark9159 said:
im having trouble setting my TI-83 Plus into "degree mode"

Press [MODE] and cursor down and right to the word Degree and hit [ENTER]

thank you very much

hahahhahah. are you in the BYU online homeschool thing too?

## What is a critical angle?

A critical angle is the angle of incidence at which light is refracted at an angle of 90 degrees, and no longer passes through the interface between two mediums. It marks the boundary between total internal reflection and partial reflection.

## How do you calculate the critical angle?

The critical angle can be calculated using Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two mediums.

## What is the index of refraction?

The index of refraction is a measure of how much a substance can bend light. It is the ratio of the speed of light in a vacuum to the speed of light in the substance. Different substances have different refractive indices, which can affect how light travels through them.

## How does the index of refraction affect the critical angle?

The higher the index of refraction, the smaller the critical angle will be. This means that light is more likely to undergo total internal reflection and less likely to be refracted when passing through the interface between two mediums with a higher refractive index difference.

## What are some real-world applications of finding critical angles and index of refraction?

These concepts are important in fields such as optics, telecommunications, and medicine. They are used to design and improve lenses, fiber optics, and medical imaging devices. Understanding these principles can also help in the development of new materials with specific optical properties.

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