Solve Refraction Problem 4: Find Angle of Refraction from Air to Glass

[mustang]

problem 4.
A ray of light traveling in air strikes a flat 2.00 cm tick block of glass (n=1.50) at an angle of 25.6 degrees with the normal.
Trace the light ray through the glass, and find the angle of refraction for light passing from air to glass. Answer in degrees.
Note: I don't know where to start.
Problem 6.
The angle of incidence and the angle of refraction for light going from air into a material with a higher index of refraction are 66.1 degrees and 42.2 degrees, respectively.
What is the index of refraction of this material?
Note: what formula should I use?

 

[himanshu121]

Use Snell's Law

 

[mustang]

angle problems

Problem 13.
A ray of light traveling in air strikes the midpoint of one face of an equiangular glass prism (n=1.65) at angle of exactly 30.0 degrees.
Trace the path of the light ray through the glass and find the angle of incidence of the ray at the bottom of the prism. Answer in degrees.
Note: The triangle is 60-60-60 degrees.


Problem 15.
Light strikes the surface of a prism, n=1.78. If the prism is surrounded by a fluid, what is the maximum index of refraction of the fluid that will still cause total internal reflection within the prism?
Note: The triangle is 90-45-45 triangle.

 

[_cozitsme]

For problem 4:
Given: Angle of incidence = 25.6 degrees
n1 or medium1 = 1.00 (air)
n2 or medium2 = 1.50 (glass)
Required: Angle of Refraction
Equation: n1 x sin (angle of incidence) = n2 x sin (angle of refraction)
Derivation of the formula to get the angle of refraction:
Angle of Refraction = { n1 x sin (angle of incidence) / n2 } sin ^-1
Note: when we transpose the sin from one side to one another it becomes sin^-1
Solution: (Substitution)
Angle of Refraction = { 1.00 x sin (25.6) / 1.50 } sin^-1

Angle of Refraction = 16.74 degrees or 16 degrees, 44 minutes and 30.04 seconds in DMS

Why don't you try doing problem 6 for on your own this time? You will only need to do the same. Good luck..take note of the formula.. :) HInt: the new formula you're going to use is

n2 = n1 x sin (angle of incidence) / sin (angle of refraction) :)

 

[rwisz]

To solve Refraction Problem 4, we can use 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 velocities of light in the two media. In this case, we can represent it as sin(θ1)/sin(θ2) = v1/v2, where θ1 is the angle of incidence, θ2 is the angle of refraction, v1 is the velocity of light in air, and v2 is the velocity of light in glass.

First, we need to convert the given angle of incidence from degrees to radians by multiplying it by π/180. So, θ1 = 25.6° x π/180 = 0.446 radians.

Next, we can use the refractive index (n) of glass, which is 1.50, to calculate the velocity of light in glass. We know that v = c/n, where c is the speed of light in vacuum (3 x 10^8 m/s). So, v2 = (3 x 10^8 m/s)/1.50 = 2 x 10^8 m/s.

Now, we can plug in the values in the Snell's Law equation and solve for θ2.

sin(0.446)/sin(θ2) = (3 x 10^8 m/s)/(2 x 10^8 m/s)

sin(θ2) = (2 x 10^8 m/s)/(3 x 10^8 m/s) x sin(0.446)

sin(θ2) = 0.666 x sin(0.446)

sin(θ2) = 0.296

θ2 = sin^-1(0.296)

θ2 = 17.4°

Therefore, the angle of refraction for light passing from air to glass is 17.4 degrees.

For Problem 6, we can use the same formula, Snell's Law, to solve for the index of refraction (n) of the material. So, we can represent it as sin(θ1)/sin(θ2) = v1/v2 = n2/n1, where n1 is the index of refraction of air (1.00) and n2 is the index of refraction of the material we are trying to find.

Sub