What Angle Does Light Refract in Ice?

[tymartin]

Homework Statement

A beam of sunlight with a wavelength of 500 nm strikes an ice floe at an angle of 66.5 If ice has an index of refraction n=1.31, at what angle is the beam refracted?

Homework Equations

Law of Refraction- n(i) sin 0(i)=n (r) 0 (r')

The Attempt at a Solution

I'm completely lost. I am not familiar with the sin key.

 

[tiny-tim]

Welcome to PF!

A beam of sunlight with a wavelength of 500 nm strikes an ice floe at an angle of 66.5 If ice has an index of refraction n=1.31, at what angle is the beam refracted?
…
I'm completely lost. I am not familiar with the sin key.

Hi tymartin! Welcome to PF!

(have a theta: θ and a degrees: ° )

This is Snell's law …

key in 66.5, make sure your calculator is using degrees ("deg") not radians ("rad"), and press "sin" …

that gives you sin65.5º …

now find the sin of the angle of refraction, key it in, and find the thing on your calculator that converts the "sin" key to inverse sin (sin^-1), and press the "sin" key again

 

[nlightner]

I would suggest breaking down the problem into smaller parts and utilizing the known equations and principles of refraction to solve it. Firstly, we know that the index of refraction (n) of ice is 1.31. This means that light travels slower in ice compared to air, causing it to bend or refract when passing through the ice.

Next, we can use the law of refraction, also known as Snell's law, which states that the ratio of the sine of the angle of incidence (i) to the sine of the angle of refraction (r) is equal to the ratio of the indices of refraction of the two media (n). In mathematical terms, this can be written as n1 sin i = n2 sin r, where n1 and n2 are the indices of refraction of the two media, and i and r are the angles of incidence and refraction, respectively.

Now, we can plug in the given values into the equation:
n1 = 1 (since the light is coming from air)
n2 = 1.31 (index of refraction of ice)
i = 66.5 degrees
r = unknown (what we are trying to find)

So, we have:
1 sin 66.5 = 1.31 sin r
sin 66.5 = 1.31 sin r
sin r = (sin 66.5)/1.31
r = sin^-1 [(sin 66.5)/1.31]
r = 45.27 degrees

Therefore, the angle of refraction is approximately 45.27 degrees.

I hope this helps you understand the concept of refraction and how to solve problems related to it. Remember, as a scientist, it is important to break down complex problems into smaller, more manageable parts and use known principles and equations to find solutions.