Calculating Wavelengths & Refraction Angles for Violet Light

[wikidrox]

Here is the question:
Violet light has a frequency of 7.5 * 10^14 hz and travels from air to glass at an angle of 30 degrees. The index of refraction for violet light is 1.54.
A) Find the angle of refraction
B) Find the wavelength in air
C) Find the wavelength in glass
D) What is the speed of propagation in glass.

I was able to find the angle of refraction to be 19 degrees. But now I don't know how to find the wavelengths in each of the mediums. Can someone help me?

 

[Doc Al]

wave equation

Apply the wave equation: V = f*λ, where V is the speed of light in the medium. Realize that the speed of light in glass is slower than in air by a factor equal to the index of refraction. The frequency of light remains unchanged as it passes from air to glass.

 

[M98Ranger]

A) To find the angle of refraction, we can use the Snell's Law equation: n1sinθ1 = n2sinθ2. Where n1 is the index of refraction of the first medium (air) and n2 is the index of refraction of the second medium (glass). θ1 is the angle of incidence (30 degrees) and θ2 is the angle of refraction (to be found). So we have: 1 x sin30 = 1.54 x sinθ2. Solving for θ2, we get θ2 = 19 degrees.

B) To find the wavelength in air, we can use the formula: λ = c/f, where λ is the wavelength, c is the speed of light (3 x 10^8 m/s) and f is the frequency (7.5 x 10^14 Hz). So, λ = (3 x 10^8 m/s) / (7.5 x 10^14 Hz) = 4 x 10^-7 m or 400 nm.

C) To find the wavelength in glass, we can use the formula: λ = λ0 / n, where λ is the wavelength in glass, λ0 is the wavelength in air (found in part B) and n is the index of refraction of glass (1.54). So, λ = (400 nm) / (1.54) = 260.4 nm.

D) The speed of propagation in glass can be calculated using the formula: v = c/n, where v is the speed of propagation in glass, c is the speed of light and n is the index of refraction of glass. So, v = (3 x 10^8 m/s) / (1.54) = 1.9487 x 10^8 m/s or 194.87 x 10^6 m/s.

 

[M98Ranger]

Sure, I'd be happy to help you with the rest of the calculations. Let's start with finding the wavelength in air.

A) To find the angle of refraction, we can use Snell's law: n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two mediums, and θ1 and θ2 are the angles of incidence and refraction, respectively. Plugging in the values given, we get:

1.00sin30 = 1.54sinθ2
sinθ2 = 0.649
θ2 = sin^-1(0.649) = 40.6 degrees

B) Now, to find the wavelength in air, we can use the equation: λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency. Plugging in the values given, we get:

λ = (3.00 * 10^8 m/s) / (7.5 * 10^14 Hz)
λ = 4.00 * 10^-7 m = 400 nm

C) To find the wavelength in glass, we can use the equation: n1λ1 = n2λ2, where n1 and n2 are the refractive indices of the two mediums, and λ1 and λ2 are the wavelengths in the first and second medium, respectively. Plugging in the values given, we get:

1.00(400 nm) = 1.54λ2
λ2 = (400 nm) / (1.54) = 260 nm

D) The speed of propagation in glass can be found using the equation: v = c/n, where v is the speed of light in the medium, c is the speed of light in vacuum, and n is the refractive index of the medium. Plugging in the values given, we get:

v = (3.00 * 10^8 m/s) / (1.54)
v = 1.95 * 10^8 m/s

I hope this helps! Let me know if you have any further questions.