A ray of light approaches a jar of honey at an angle of 30.0 degrees. If the angle of refraction is 19.5 degrees, what is the refractive index of honey?

To find the refractive index of honey, we can use Snell's law.

Snell's law 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.

In this case, we are given the angle of incidence (30.0 degrees) and the angle of refraction (19.5 degrees). We need to find the refractive index of honey.

The refractive index of a medium (in this case honey) is defined as the ratio of the speed of light in vacuum to the speed of light in that medium.

Let's denote the refractive index of honey as n and the speed of light in vacuum as c.

Using Snell's law, we have:

sin(angle of incidence) / sin(angle of refraction) = speed of light in vacuum / speed of light in honey

sin(30.0 degrees) / sin(19.5 degrees) = c / speed of light in honey

Using trigonometric identities, we can simplify this equation:

(0.5) / (sin 19.5 degrees) = c / speed of light in honey

Now, rearranging the equation to solve for the refractive index of honey:

speed of light in honey = c / (0.5 / sin 19.5 degrees)

To calculate the refractive index, we need to know the speed of light in vacuum (c) and the value of sin(19.5 degrees). The speed of light in vacuum is approximately 3.0 x 10^8 m/s.

By substituting these values into the equation, we can find the refractive index of honey.

To find the refractive index of honey, we can use Snell's law, which relates the angles of incidence and refraction to the refractive index:

n1 * sin(θ1) = n2 * sin(θ2),

where:
- n1 is the refractive index of the medium the ray is coming from (in this case, air),
- θ1 is the angle of incidence,
- n2 is the refractive index of the medium the ray is entering (here, honey), and
- θ2 is the angle of refraction.

Here, we know the angle of incidence (θ1) is 30.0 degrees, and the angle of refraction (θ2) is 19.5 degrees.

Since the ray is coming from air, we can take the refractive index of air to be approximately 1.0.

Plugging this information into Snell's law, we have:

1.0 * sin(30.0 degrees) = n2 * sin(19.5 degrees).

To find n2, we can rearrange the equation:

n2 = (1.0 * sin(30.0 degrees)) / sin(19.5 degrees).

Using a scientific calculator, we can evaluate this expression:

n2 = (1.0 * 0.5) / 0.332 = 1.51 (rounded to two decimal places).

Therefore, the refractive index of honey is approximately 1.51.

I assume the 30 degrees is the angle to the normal; also I assume you are neglecting the effects of the container holding the honey.

n1*sin 30 = n2*sin 19.5
n1 is 1 for air.
Solve for n2.