To find the critical angle in total internal reflection problems, the following equation must be used:

 where the subscripts  stands for critical,  stands for refraction, and  stands for incident index of refraction. 

Plug in the values and solve for the critical angle:

Here, the incident index of refraction belongs to water.

For this question, we're told that light is traveling from one medium into another one. We're given the indices of refraction for both media, as well as the incident angle with respect to the normal, and we're asked to find the critical angle.

It's important to remember that when light crosses from one medium into a different one, the speed at which the light travels will change. Depending on how fast the light travels in a given medium compared to its speed in a vacuum will determine its index of refraction. In a denser medium, the light will bend towards the normal more heavily, while in a less dense medium it will bend farther from the normal.

For there to be a critical angle, light must travel from a medium of greater density to a medium of lesser density. In other words, the light must travel from a medium with a higher index of refraction into one with a lower index of refraction. Hence, there will not be a critical angle if the ray of light is traveling from a medium with a low index of refraction to a second medium with a higher index of refraction. In the question stem, this is exactly what is happening. Consequently, there cannot be a critical angle.

Write the formula relating the speed of light, velocity of light in specific medium, and index of refraction of the medium.

Rewrite the equation so that we are solving for the velocity of light in water. Substitute given values.

To find the index of refraction given two angles and another index of refraction, we use Snell's law.

We can plug in the numbers we have to find the answer.

Simplifying, we get:

To find the angle of incidence, we use Snell's law.

We're given both indices of refraction, and the second angle, so we can plug in our numbers.

Therefore, the angle of incidence is .

First off we can find the velocity of the laser beam since we know the distance of honey it travels through and the transit time.

However, this doesn't need to be explicitly solved for. The velocity of light inside a material is inversely proportional to the index of refraction of that material where

where  is the speed of light in vacuum. Setting these equal, we can solve for the index of refraction of the honey.

We expect that the index of refraction will be greater than that of air and a velocity less than .

The speed of light passing through a medium is given by:

Rearrange to solve for the index of refraction and plug in numbers.

To have total internal reflection, our equation will become:

We can use our knowledge about the indices of refraction to come up with our equation:

, where  is the index of refraction of air and  is the index of refraction for our alcohol. 

Since 

For this question, we're told that light is passing from air into another medium. In doing so, the light is refracted such that it bends away from the normal. We're asked to identify a possible medium.

The most important thing to understand about refraction is that when light passes into a new medium at an angle with respect to the normal, that light will be refracted, either away from or toward the normal. This is because light will travel through different media at different speeds. The faster light travels, the more it will bend away from the normal.

Generally, the angle at which light is bent can be predicted by Snell's law. In doing so, this equation takes use of the refractive index, a value unique to each medium. The expression for refractive index is as follows.

Where  refers to the refractive index,  refers to the speed of light in a vacuum, and  refers to the speed of light in a given medium.

Since the speed of light is fastest when in a vacuum, the refractive index can never be less than . Only when the light is in a vacuum is the refractive index equal to . In any other medium, the refractive index will be greater than , even if it is slight.

Light will always refract away from the normal when it passes into a medium with a lower refractive index (indicating the light is traveling faster). Starting from air, the only way this can happen is for the new medium to have an index of refraction that is less than air. Of the answer choices shown, the only one that fits that criteria is the vacuum.