Angle of Refraction Given Wavelength & Speed of Light in Air & Glass

In summary: DEG button, not the RAD button! :wink:)In summary, the problem involves a light ray of 600 nm wavelength entering a piece of glass with a speed of 0.650 times that in air. Using Snell's Law and the given angle of incidence of 40 degrees, we can calculate the angle of refraction to be approximately 24.7 degrees. However, the individual asking for help has encountered difficulties in setting up the problem, possibly due to using radians instead of degrees on their calculator.
  • #1
Oneablegal
4
0

Homework Statement



Light of wavelength 600 nm in air enters a piece of glass. The speed of light in this glass is 0.650 times the speed in air. Calculate the angle of refraction, Given that the angle of incidence of this light ray is 40°.

Homework Equations


Snell's Law
Sin(θ1)/sin(θ2) = v1/v2


The Attempt at a Solution



I calculated the wavelength to be 390 nm. (600nm x 0.65). I know the Speed of light in glass is less than an air so light is going to slow down and bend towards the normal, therefore the angle of refraction will be less then the incident 40°. I know the practice problem answer is 24.7 degrees. I need help bridging the gap, so to understand this problem. Please help! Thank you in advance.
 
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  • #2
Hi Oneablegal! :smile:

First … did you set your calculator to degrees (not radians)? :wink:

(If so, please show how far you've got.)
 
  • #3
tiny-tim said:
Hi Oneablegal! :smile:

First … did you set your calculator to degrees (not radians)? :wink:

(If so, please show how far you've got.)
Hi! Yes, the calculator is set to degrees. This is as far as I have gotten. I have tried to set this up numerous times, with angle 1 set equal to sin(40) or 0.745113. Angle 2 or the angle of refraction is unknown. V1 I have as 1.00 and V2 as 0.65. I am lost from here...

Thanks again!
 
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  • #4
Hi Oneablegal! :smile:

(just got up :zzz:)
Oneablegal said:
Hi! Yes, the calculator is set to degrees.

…with angle 1 set equal to sin(40) or 0.745113

he he! :biggrin:

No it isn't!

sin(40 radians) = 0.745113 :wink:
 
  • #5


I would approach this problem by 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 velocities of light in the two mediums. In this case, we know the angle of incidence (40°) and the velocity of light in air (c), so we can plug those values into the equation:

sin(40°)/sin(θ2) = c/0.650c

We can simplify this by dividing both sides by c and multiplying by 0.650:

sin(40°)/0.650 = sin(θ2)

Now, we can use the inverse sine function to solve for the angle of refraction (θ2):

sin^-1(sin(40°)/0.650) = θ2

Plugging this into a calculator, we get an angle of refraction of approximately 24.7°, which matches the given answer.

In summary, by using Snell's Law and the given values of angle of incidence and velocity of light in air and glass, we can calculate the angle of refraction to be 24.7°. This is because light slows down and bends towards the normal when it enters a medium with a lower velocity, such as glass.
 

FAQ: Angle of Refraction Given Wavelength & Speed of Light in Air & Glass

1. What is the formula for calculating the angle of refraction given the wavelength and speed of light in air and glass?

The formula for calculating the angle of refraction is sin(θ2) = (n1/n2) * sin(θ1), where θ1 is the angle of incidence, θ2 is the angle of refraction, n1 is the refractive index of the medium the light is coming from (air), and n2 is the refractive index of the medium the light is entering (glass).

2. How do I determine the refractive index of air and glass?

The refractive index of air is approximately 1.0003, which can be rounded to 1 for most calculations. The refractive index of glass varies depending on the type of glass, but it is typically between 1.45 and 1.9. You can find the exact refractive index of a specific type of glass by researching its material properties or consulting a reference table.

3. Can the angle of refraction ever be greater than the angle of incidence?

No, the angle of refraction can never be greater than the angle of incidence. This is known as 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 always equal to the ratio of the refractive indices of the two media. This means that as the angle of incidence increases, the angle of refraction will also increase, but it will never be greater than the angle of incidence.

4. How does the speed of light in a medium affect the angle of refraction?

The speed of light in a medium is directly related to the refractive index of that medium. As the speed of light decreases, the refractive index increases, and therefore the angle of refraction will also increase. This is because light travels slower in a medium with a higher refractive index, causing it to bend more when entering that medium.

5. What is the relationship between the wavelength of light and the angle of refraction?

The wavelength of light has no direct effect on the angle of refraction. The angle of refraction is determined by the refractive indices of the two media and the angle of incidence. However, the wavelength of light does affect the speed of light in a medium, which in turn affects the angle of refraction. Shorter wavelengths (such as blue light) will have a higher refractive index and therefore a larger angle of refraction compared to longer wavelengths (such as red light).

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