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A laser beam is incident at an angle of 29.2° to the vertical onto a solution of corn syrup in water.
(a) If the beam is refracted to 19.16° to the vertical, what is the index of refraction of the syrup solution?


(b) Suppose the light is red, with wavelength 632.8 nm in a vacuum. Find its wavelength in the solution.
nm

(c) Find its frequency in the solution.
Hz

(d) Find its speed in the solution.
m/s

A laser beam is incident at an angle of 292 to the vertical onto a solution of corn syrup in water a If the beam is refracted to 1916 to the vertical what is th class=

Respuesta :

michaellj973

Answer:

Explanation:

To solve this problem, we can use Snell's Law, which relates the angles and indices of refraction of light as it passes from one medium to another:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

where:

n₁ is the index of refraction of the incident medium (in this case, air or vacuum)

θ₁ is the angle of incidence

n₂ is the index of refraction of the refracted medium (in this case, the syrup solution)

θ₂ is the angle of refraction

Let's solve each part of the problem step by step:

Part (a):

We are given:

θ₁ = 29.2°

θ₂ = 19.16°

Let's assume the index of refraction of air or vacuum is 1 (since no value is provided).

Using Snell's Law, we have:

1 * sin(29.2°) = n₂ * sin(19.16°)

Solving for n₂:

n₂ = (sin(29.2°) / sin(19.16°))

Part (b):

We are given:

Wavelength in vacuum (λ₀) = 632.8 nm

The relationship between the wavelength in vacuum (λ₀) and the wavelength in the syrup solution (λ) can be expressed as:

λ / λ₀ = n₂

Solving for λ:

λ = λ₀ * n₂

Part (c):

The frequency of light (f) remains constant when it passes from one medium to another. So, the frequency in the syrup solution (f) is the same as the frequency in vacuum (f₀).

Part (d):

The speed of light in a medium is given by the equation:

v = c / n₂

where:

v is the speed of light in the medium

c is the speed of light in a vacuum (approximately 3 x 10^8 m/s)

Let's calculate the values now.

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