A ray of light of frequency 5.09 x 10^14 Hz passes from air into flint glass (n=1.6).
a.) If the ray enters the flint glass at an angle of 30*, what is the angle of refraction?
b.) What is the critical angle for a ray of light traveling from flint glass to air?
c.) What is the speed of light in flint glass?
d.) What is the wavelength of this light ray in air?
I suggest that you review Snell's Law for (a) and (b) and the definition of Index of Refraction for (c). For (d), use the equation (wavelength)*frequency) = (speed of light)
Frequency is a constant.
a.) The angle of refraction is approximately 19.5°.
b.) The critical angle for a ray of light traveling from flint glass to air is approximately 41.8°.
c.) The speed of light in flint glass is approximately 1.9 x 10^8 m/s.
d.) The wavelength of this light ray in air is approximately 5.94 x 10^-7 m.
Sure! Let's go step by step:
a) To determine the angle of refraction, we can use Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two media.
Snell's Law: n1*sin(theta1) = n2*sin(theta2)
Here, n1 and n2 are the indices of refraction of the two media, and theta1 and theta2 are the angles of incidence and refraction, respectively.
Given:
n1 (air) = 1.00
theta1 = 30°
n2 (flint glass) = 1.6 (index of refraction of flint glass)
Using the given values, we can rearrange Snell's Law to solve for theta2:
sin(theta2) = (n1/n2) * sin(theta1)
sin(theta2) = (1.00/1.6) * sin(30°)
sin(theta2) = 0.625 * 0.5
sin(theta2) = 0.3125
Now, we need to find the angle whose sine is equal to 0.3125. Using inverse sine (sin^-1) function, we can find the angle:
theta2 = sin^-1(0.3125)
theta2 ≈ 18.19°
Therefore, the angle of refraction is approximately 18.19°.
b) To find the critical angle, we can use the formula:
critical angle = sin^-1(1/n)
Given n (flint glass) = 1.6, we can substitute the value into the formula:
critical angle = sin^-1(1/1.6)
critical angle ≈ 39.81°
Therefore, the critical angle for a ray of light traveling from flint glass to air is approximately 39.81°.
c) The speed of light in a medium can be calculated using the formula:
speed of light in a medium = (speed of light in a vacuum)/index of refraction
The speed of light in a vacuum is a constant, denoted by "c". Its value is approximately 3.00 x 10^8 m/s.
Given n (flint glass) = 1.6, we can substitute the values into the formula:
speed of light in flint glass = (3.00 x 10^8 m/s)/1.6
speed of light in flint glass ≈ 1.88 x 10^8 m/s
Therefore, the speed of light in flint glass is approximately 1.88 x 10^8 m/s.
d) To find the wavelength of the light ray in air, we can use the equation:
wavelength = (speed of light)/(frequency)
Given frequency = 5.09 x 10^14 Hz, we can substitute the value into the equation:
wavelength = (3.00 x 10^8 m/s)/(5.09 x 10^14 Hz)
wavelength ≈ 5.89 x 10^-7 m
Therefore, the wavelength of this light ray in air is approximately 5.89 x 10^-7 m.
a.) To find the angle of refraction, 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 speeds of light in the two media.
Snell's Law:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Given:
n₁ (index of refraction in air) = 1.0
n₂ (index of refraction in flint glass) = 1.6
θ₁ (angle of incidence) = 30°
To find θ₂ (angle of refraction), we can rearrange the equation as follows:
sin(θ₂) = (n₁/n₂) * sin(θ₁)
sin(θ₂) = (1.0/1.6) * sin(30°)
sin(θ₂) = 0.625 * 0.5
Now, we need to find the inverse sine (also known as arcsine) of the value:
θ₂ = arcsin(0.625 * 0.5)
Using a calculator, we can find that θ₂ ≈ 23.6°.
Therefore, the angle of refraction is approximately 23.6°.
b.) The critical angle occurs when the angle of refraction is 90°. In this case, the ray of light is going from flint glass to air.
Using Snell's law with θ₁ = 90°:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
1.6 * sin(90°) = 1.0 * sin(θ₂)
Since sin(90°) = 1, the equation becomes:
1.6 * 1 = sin(θ₂)
Now, we need to find the inverse sine of the value:
θ₂ = arcsin(1.6)
Using a calculator, we can find that θ₂ ≈ 70.53°.
Therefore, the critical angle for the ray of light traveling from flint glass to air is approximately 70.53°.
c.) The index of refraction, n, for a given medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium.
n = c/v
Where c is the speed of light in vacuum and v is the speed of light in the medium.
In this case, the speed of light in air is approximately the same as the speed of light in vacuum, so we can use c as the speed of light in air.
n = c/v
1.6 = c/v
To find the speed of light in flint glass, we rearrange the equation:
v = c/n
v = c/1.6
Note that the speed of light in vacuum or air is approximately 3 x 10^8 meters per second.
v ≈ (3 x 10^8 m/s) / 1.6
Using a calculator, we find that the speed of light in flint glass is approximately 1.875 x 10^8 meters per second.
Therefore, the speed of light in flint glass is approximately 1.875 x 10^8 m/s.
d.) The wavelength of a light ray can be found using the formula:
wavelength = (speed of light) / (frequency)
Given:
frequency = 5.09 x 10^14 Hz
Using the known speed of light in air or vacuum, we can calculate the wavelength:
wavelength = (speed of light) / (frequency)
wavelength ≈ (3 x 10^8 m/s) / (5.09 x 10^14 Hz)
Using a calculator, we find that the wavelength of this light ray in air is approximately 5.89 x 10^-7 meters (or 589 nm).
Therefore, the wavelength of this light ray in air is approximately 5.89 x 10^-7 meters (or 589 nm).