Index of Refraction - AP Physics 2

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Question

The speed of light in a vacuum, , is calculated to be $2.99 \cdot 10^8 \frac{m}{s}$ . The speed of light in a diamond is calculated to be $1.25 \cdot 10^8 \frac{m}{s}$ . What is the refractive index of diamond?

Answer

The definition of refractive index of a medium is the speed of light in a vacuum divided by the speed of light in the medium:

$n = \frac{c}{v}$

We have values for and , so we can plug in our numbers into the equation.

$n&=\frac{2.99\cdot 10^8\ \frac{m}{s}}{1.25\cdot 10^8\ \frac{m}{s}}$

Because we're dividing two values with the same units, our answer is unitless.

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Question

What is the speed at which light travels through the water?

$c=3 *10^8:\frac{m}{s}$ and $n_{water}=1.33$

Answer

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

$n_{material}=\frac{c}{v}$

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

$v=\frac{c}{n_{water}}=\frac{3 * 10^8 \frac{m}{s}}{1.33}=2.26 * 10^8\frac{m}{s}$

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Question

A beam of light travelling through air enters a transparent material at an angle of incidence at $34^{\textup o}$ , with the refracted beam's angle being $26^{\textup o}$ . What is the index of refraction of the material? Assume the index of refraction of air is 1.

Answer

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

$\begin{align} n_1\sin\theta_1&=n_2\sin\theta_2 \ \frac{n_1\sin\theta_1}{\sin\theta_2}&= n_2 \end{align}$

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

$\frac{n_1\sin\theta_1}{\sin\theta_2}&= n_2$

$\frac{(1)(\sin(34^o))}{\sin(26^o)}&=n_2$

Simplifying, we get:

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Question

A beam of light travelling through air enters a medium with an index of refraction of and goes through it at an angle of $41^{\text o}$ . What is the angle of incidence?

Assume the index of refraction of air is 1.

Answer

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

$n_1\sin\theta_1&=n_2\sin\theta_2$

$\sin\theta_1&=\frac{n_2\sin\theta_2}{n_1}$

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

$\sin\theta_1=\frac{n_2\sin\theta_2}{n_1}$

$\sin \theta_1=\frac{(1.51)(\sin(41^o))}{1}$

$\theta_1 = 82.16^{\text o}$

Therefore, the angle of incidence is $82.16^{\textup o}$ .

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Question

An argon/krypton laser puts out green light at . It takes to travel through of honey. What is the index of refraction of the honey?

Answer

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.

$v=\frac{d}{t}$

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

$v_{honey}=\frac{c}{n_{honey}}$

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

$\frac{d}{t}=\frac{c}{n_{honey}}$

$n_{honey}=\frac{c t}{d}=1.47$

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

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Question

The speed of light through a particular material is measured to be $v=2.5 * 10^{8} \frac{m}{s}$ , calculate the index of refraction of the material.

Answer

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

$v_{light,n}=\frac{c}{n}$

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

$n=\frac{c}{v_{light,n}}=\frac{3.0\times 10^{8}\frac{m}{s}}{2.5\times 10^{8}\frac{m}{s}}=1.2$

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Question

You are passing a ray of light through clear alcohol to determine properties. You shine the light ray exactly to the surface of alcohol.

Determine the index of refraction of alcohol if the light ray bends to to the normal. Assume index of refraction of air is .

Answer

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

$\frac{sin(45^o)}{sin(22^o)}=n_2=1.9$

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Question

You are passing a ray of light through clear alcohol to determine properties. You shine the light ray exactly to the surface of alcohol.

Determine the index of refraction required in the alcohol to have total internal reflection?

Answer

To have total internal reflection, our equation will become:

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Question

Suppose that a ray of light traveling through air strikes a new medium. Upon doing so, the light bends away from the normal. Which of the following could this new medium be?

Answer

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.

$n=\frac{c}{v}$

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.

Compare your answer with the correct one above

Question

The speed of light in a vacuum, , is calculated to be $2.99 \cdot 10^8 \frac{m}{s}$ . The speed of light in a diamond is calculated to be $1.25 \cdot 10^8 \frac{m}{s}$ . What is the refractive index of diamond?

Answer

The definition of refractive index of a medium is the speed of light in a vacuum divided by the speed of light in the medium:

$n = \frac{c}{v}$

We have values for and , so we can plug in our numbers into the equation.

$n&=\frac{2.99\cdot 10^8\ \frac{m}{s}}{1.25\cdot 10^8\ \frac{m}{s}}$

Because we're dividing two values with the same units, our answer is unitless.

Compare your answer with the correct one above

Question

What is the speed at which light travels through the water?

$c=3 *10^8:\frac{m}{s}$ and $n_{water}=1.33$

Answer

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

$n_{material}=\frac{c}{v}$

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

$v=\frac{c}{n_{water}}=\frac{3 * 10^8 \frac{m}{s}}{1.33}=2.26 * 10^8\frac{m}{s}$

Compare your answer with the correct one above

Question

A beam of light travelling through air enters a transparent material at an angle of incidence at $34^{\textup o}$ , with the refracted beam's angle being $26^{\textup o}$ . What is the index of refraction of the material? Assume the index of refraction of air is 1.

Answer

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

$\begin{align} n_1\sin\theta_1&=n_2\sin\theta_2 \ \frac{n_1\sin\theta_1}{\sin\theta_2}&= n_2 \end{align}$

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

$\frac{n_1\sin\theta_1}{\sin\theta_2}&= n_2$

$\frac{(1)(\sin(34^o))}{\sin(26^o)}&=n_2$

Simplifying, we get:

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Question

A beam of light travelling through air enters a medium with an index of refraction of and goes through it at an angle of $41^{\text o}$ . What is the angle of incidence?

Assume the index of refraction of air is 1.

Answer

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

$n_1\sin\theta_1&=n_2\sin\theta_2$

$\sin\theta_1&=\frac{n_2\sin\theta_2}{n_1}$

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

$\sin\theta_1=\frac{n_2\sin\theta_2}{n_1}$

$\sin \theta_1=\frac{(1.51)(\sin(41^o))}{1}$

$\theta_1 = 82.16^{\text o}$

Therefore, the angle of incidence is $82.16^{\textup o}$ .

Compare your answer with the correct one above

Question

An argon/krypton laser puts out green light at . It takes to travel through of honey. What is the index of refraction of the honey?

Answer

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.

$v=\frac{d}{t}$

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

$v_{honey}=\frac{c}{n_{honey}}$

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

$\frac{d}{t}=\frac{c}{n_{honey}}$

$n_{honey}=\frac{c t}{d}=1.47$

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

Compare your answer with the correct one above

Question

The speed of light through a particular material is measured to be $v=2.5 * 10^{8} \frac{m}{s}$ , calculate the index of refraction of the material.

Answer

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

$v_{light,n}=\frac{c}{n}$

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

$n=\frac{c}{v_{light,n}}=\frac{3.0\times 10^{8}\frac{m}{s}}{2.5\times 10^{8}\frac{m}{s}}=1.2$

Compare your answer with the correct one above

Question

You are passing a ray of light through clear alcohol to determine properties. You shine the light ray exactly to the surface of alcohol.

Determine the index of refraction of alcohol if the light ray bends to to the normal. Assume index of refraction of air is .

Answer

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

$\frac{sin(45^o)}{sin(22^o)}=n_2=1.9$

Compare your answer with the correct one above

Question

You are passing a ray of light through clear alcohol to determine properties. You shine the light ray exactly to the surface of alcohol.

Determine the index of refraction required in the alcohol to have total internal reflection?

Answer

To have total internal reflection, our equation will become:

Compare your answer with the correct one above

Question

Suppose that a ray of light traveling through air strikes a new medium. Upon doing so, the light bends away from the normal. Which of the following could this new medium be?

Answer

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.

$n=\frac{c}{v}$

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.

Compare your answer with the correct one above

Question

The speed of light in a vacuum, , is calculated to be $2.99 \cdot 10^8 \frac{m}{s}$ . The speed of light in a diamond is calculated to be $1.25 \cdot 10^8 \frac{m}{s}$ . What is the refractive index of diamond?

Answer

The definition of refractive index of a medium is the speed of light in a vacuum divided by the speed of light in the medium:

$n = \frac{c}{v}$

We have values for and , so we can plug in our numbers into the equation.

$n&=\frac{2.99\cdot 10^8\ \frac{m}{s}}{1.25\cdot 10^8\ \frac{m}{s}}$

Because we're dividing two values with the same units, our answer is unitless.

Compare your answer with the correct one above

Question

What is the speed at which light travels through the water?

$c=3 *10^8:\frac{m}{s}$ and $n_{water}=1.33$

Answer

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

$n_{material}=\frac{c}{v}$

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

$v=\frac{c}{n_{water}}=\frac{3 * 10^8 \frac{m}{s}}{1.33}=2.26 * 10^8\frac{m}{s}$

Compare your answer with the correct one above

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