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

[Oneablegal]

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.

 

[tiny-tim]

Hi Oneablegal!

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

(If so, please show how far you've got.)

 

[Oneablegal]

Hi Oneablegal!

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

(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!

 

[tiny-tim]

Hi Oneablegal!

(just got up :zzz:)

Hi! Yes, the calculator is set to degrees.

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

he he!

No it isn't!

sin(40 radians) = 0.745113 ​

 

[HalfLostAndSearching]

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.