Question 1

Light enters a substance from air at $30.0 ^ { \circ }$ to the normal. It continues within the substance at $23.0 ^ { \circ }$ to the normal. What is the critical angle for this substance when it is surrounded by air?

Accepted Answer

The critical angle can be found using Snell's Law: $ n_1 \sin \theta_1 = n_2 \sin \theta_2 $. Given $ \theta_1 = 30.0^\circ $ and $ \theta_2 = 23.0^\circ $, we find the refractive index $ n_2 $ of the substance. The critical angle $ \theta_c $ is then found using $ \sin \theta_c = \frac{1}{n_2} $. Solving gives $ \theta_c \approx 51.4^\circ $.

Question 2

Light in a transparent material that has an index of refraction of 1.333 strikes the boundary
with another transparent material for which the index of refraction is 1.010. What is the
critical angle for total internal reflection between these two materials?

Accepted Answer

The answer of Light in a transparent material that has...

Question 3

A light ray enters a glass enclosed fish tank. From air it enters the glass at 20° with respect
to the plane of the surface and then emerges into the water. The index for the glass is 1.50
and for water 1.33.
(a) What is the angle of refraction in the glass?
(b) What is the angle of refraction in the water?
(c) Is there any incident angle in air for which the ray will not enter the water due to total
internal reflection? If so, find it.

Accepted Answer

The answer of A light ray enters a glass enclosed...

Question 4

Light travels from crown glass, with a refractive index of $1.52$, into water, having a refractive index of $1.33$ ? The critical angle for this interface is closest to which one of the following angles?

Accepted Answer

The answer of Light travels from crown glass, with a...

Question 5

A flashlight beam makes an angle of 60° with the plane of the surface of a calm lake before it enters the water. In the water what angle does the beam make with the plane of the surface? The
Index of refraction of water is 1.33.

Accepted Answer

The answer of A flashlight beam makes an angle of...

Question 6

As shown in the figure, a laser positioned on a ship is used to communicate with a small research submarine resting on the bottom of a lake. The laser is positioned $12 \mathrm {~m}$ above the surface of the water, and it strikes the water $20 \mathrm {~m}$ from the side of the ship. The water is $58 \mathrm {~m}$ deep and has an index of refraction of $1.33$. How far horizontally is the submarine from the side of the ship?
(Assume all numbers are accurate to three significant figures.)

Accepted Answer

The answer of As shown in the figure, a laser...

Question 7

A point source of light is positioned $20.0 \mathrm {~m}$ below the surface of a lake. What is the diameter of the largest circle on the surface of the water through which light can emerge into the air? The index of refraction of water is $1.33 .$

Accepted Answer

The answer of A point source of light is positioned...

Question 8

An optic fiber is made of clear plastic with an index of refraction of $1.50$. For what range of angles of incidence $\theta$ with the lateral surface of the fiber will light remain inside the plastic "guide" if it is surrounded by air?

Accepted Answer

For total internal reflection to occur, the angle of incidence must be greater than the critical angle. The critical angle can be calculated using Snell's law, $n_1 \sin(\theta_c) = n_2 \sin(90^\circ)$, where $n_1$ is the index of refraction of the denser medium (plastic, 1.50), $n_2$ is the index of refraction of the less dense medium (air, approximately 1.00), and $\theta_c$ is the critical angle. Solving for $\theta_c$, we get $\sin(\theta_c) = \frac{n_2}{n_1} = \frac{1.00}{1.50}$, which gives $\theta_c \approx 41.8^\circ$. Therefore, for light to remain inside the plastic guide, the angle of incidence must be greater than this critical angle, up to 90 degrees.

Question 9

A glass plate with an index of refraction is $1.57$ is immersed in an oil having a refractive index of $1.40$. The surface of the glass is inclined at an angle of $54 ^ { \circ }$ with the vertical. A horizontal light ray in the glass strikes the interface. What is the angle that the refracted ray, in the oil, makes with the horizontal?

Accepted Answer

The answer of A glass plate with an index of...

Question 10

A light ray in glass arrives at the glass-water interface an an angle of $\theta = 48 ^ { \circ }$ with the normal. The refracted ray in water makes an angle $\phi = 72 ^ { \circ }$ angle with the normal, as shown in the figure. The index of refraction of water is $1.33$. The angle of incidence is now changed to $\theta = 37 ^ { \circ }$. What is the new angle of refraction $\phi$ in the water?

Accepted Answer

The answer of A light ray in glass arrives at...

Question 11

A beam of light traveling in air strikes a slab of transparent material. The incident beam makes an angle of $40 ^ { \circ }$ with the normal, and the refracted beam make an angle of $26 ^ { \circ }$ with the normal. What is the speed of light in the transparent material? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Accepted Answer

The speed of light in the transparent material can be calculated using Snell's Law, which states $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the refractive indices of air and the material, respectively, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction. Given that the speed of light in air (or vacuum) is $3.0 \times 10^8 m/s$ and using the refractive index relation $n = c/v$, where $c$ is the speed of light in vacuum and $v$ is the speed of light in the material, we can solve for $v$. Given the angles, we find that the speed of light in the material is $2.0 \times 10^8 m/s$, making choice B correct.

Question 12

A ray of light traveling in air makes a $63.0 ^ { \circ }$ angle with respect to the normal of the surface of a liquid. It travels in the liquid at a $39.2 ^ { \circ }$ angle with respect to the normal. Find the critical angle for total internal reflection for this interface.

Accepted Answer

The answer of A ray of light traveling in air...

Question 13

The critical angle for a substance in air is measured at $53.7 ^ { \circ }$. If light enters this substance from air at $45.0 ^ { \circ }$ with the normal, at what angle with the normal will it continue to travel?

Accepted Answer

Since the angle of incidence $45.0 ^ { \circ }$ is less than the critical angle $53.7 ^ { \circ }$, the light will refract into the substance. Using Snell's law, the angle of refraction can be calculated, resulting in an angle of $34.7 ^ { \circ }$.

Question 14

A beam of light in water (of refractive index of $1.33$ ) enters a glass slab (of refractive index $1.50$ ) at an angle of incidence of $60.0 ^ { \circ }$. What is the angle of refraction in the glass?

Accepted Answer

The answer of A beam of light in water (of...

Question 15

A beam of light in air enters a glass slab with an index of refraction of $1.40$ at an angle of incidence of $30.0 ^ { \circ }$. What is the angle of refraction?

Accepted Answer

To find the angle of refraction, we use Snell's Law, which states $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the indices of refraction of the first and second mediums respectively, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction respectively. Given $n_1 = 1$ (for air), $n_2 = 1.40$, and $\theta_1 = 30^\circ$, we solve for $\theta_2$. Rearranging the formula gives $\theta_2 = \arcsin\left(\frac{n_1}{n_2} \sin(\theta_1)\right) = \arcsin\left(\frac{1}{1.40} \sin(30^\circ)\right)$, which calculates to approximately $20.9^\circ$.

Question 16

Lucite has an index of refraction of $1.50$. What is its critical angle if it is in air?

Accepted Answer

The critical angle can be calculated using the formula $\theta_c = \sin^{-1}(\frac{n_2}{n_1})$, where $n_2$ is the index of refraction of air (1.00) and $n_1$ is the index of refraction of Lucite (1.50). This gives $\theta_c = \sin^{-1}(\frac{1.00}{1.50}) = 41.8^\circ$.

Question 17

A thick slab of plastic lies at the bottom of a tank filled with water having an index of refraction of 1.33. A narrow laser beam is shone directly downward through the water on the plastic. You then gradually rotate the laser, thereby increasing the angle with respect to the normal that it strikes the plastic. You carefully note that at the instant the beam makes an angle of $66.5 ^ { \circ }$ with the normal in the water, no light enters the plastic, but it did enter for angles smaller than that. What is the speed of light in the plastic slab? $\left( c = 3.00 \times 10 ^ { 8 } \right.$ $\mathrm { m } / \mathrm { s }$ )

Accepted Answer

The answer of A thick slab of plastic lies at...

Question 18

A thin flashlight beam traveling in air strikes a glass plate at an angle of $52 ^ { \circ }$ with the plane of the surface of the plate. If the index of refraction of the glass is $1.4$, what angle will the beam make with the normal in the glass?

Accepted Answer

The answer of A thin flashlight beam traveling in air...

Question 19

A light ray in air strikes a glass plate whose index of refraction is $1.42$. Some of the light reflects off the surface of the plate, but most of it enters the glass. If the angle of refraction is one-half the angle of reflection, the angle of refraction is closest to which one of the following angles?

Accepted Answer

The answer of A light ray in air strikes a...

Question 20

A light ray in glass arrives at the glass-water interface at an angle of $\theta = 48 ^ { \circ }$ with the normal. The refracted ray in water makes an angle $\theta = 61 ^ { \circ }$ with the normal, as shown in the figure. The index of refraction of water is $1.33$. The angle of incidence is now changed to $\theta = 25 ^ { \circ }$. What is the new angle of refraction $\phi$ in the water?

Accepted Answer

The answer of A light ray in glass arrives at...

Quiz 22: Electromagnetic Waves

Light enters a substance from air at $30.0 ^ { \circ }$ to the normal. It continues within the substance at $23.0 ^ { \circ }$ to the normal. What is the critical angle for this substance when it is surrounded by air?

Light in a transparent material that has an index of refraction of 1.333 strikes the boundary with another transparent material for which the index of refraction is 1.010. What is the critical angle for total internal reflection between these two materials?

Light travels from crown glass, with a refractive index of $1.52$ , into water, having a refractive index of $1.33$ ? The critical angle for this interface is closest to which one of the following angles?

A flashlight beam makes an angle of 60° with the plane of the surface of a calm lake before it enters the water. In the water what angle does the beam make with the plane of the surface? The Index of refraction of water is 1.33.

A point source of light is positioned $20.0 \mathrm {~m}$ below the surface of a lake. What is the diameter of the largest circle on the surface of the water through which light can emerge into the air? The index of refraction of water is $1.33 .$

An optic fiber is made of clear plastic with an index of refraction of $1.50$ . For what range of angles of incidence $\theta$ with the lateral surface of the fiber will light remain inside the plastic "guide" if it is surrounded by air?

A ray of light traveling in air makes a $63.0 ^ { \circ }$ angle with respect to the normal of the surface of a liquid. It travels in the liquid at a $39.2 ^ { \circ }$ angle with respect to the normal. Find the critical angle for total internal reflection for this interface.

The critical angle for a substance in air is measured at $53.7 ^ { \circ }$ . If light enters this substance from air at $45.0 ^ { \circ }$ with the normal, at what angle with the normal will it continue to travel?

A beam of light in water (of refractive index of $1.33$ ) enters a glass slab (of refractive index $1.50$ ) at an angle of incidence of $60.0 ^ { \circ }$ . What is the angle of refraction in the glass?

A beam of light in air enters a glass slab with an index of refraction of $1.40$ at an angle of incidence of $30.0 ^ { \circ }$ . What is the angle of refraction?

Lucite has an index of refraction of $1.50$ . What is its critical angle if it is in air?

A thin flashlight beam traveling in air strikes a glass plate at an angle of $52 ^ { \circ }$ with the plane of the surface of the plate. If the index of refraction of the glass is $1.4$ , what angle will the beam make with the normal in the glass?

Quiz 22: Electromagnetic Waves

Light enters a substance from air at 30.0∘30.0 ^ { \circ }30.0∘ to the normal. It continues within the substance at 23.0∘23.0 ^ { \circ }23.0∘ to the normal. What is the critical angle for this substance when it is surrounded by air?

Light in a transparent material that has an index of refraction of 1.333 strikes the boundary with another transparent material for which the index of refraction is 1.010. What is the critical angle for total internal reflection between these two materials?

Light travels from crown glass, with a refractive index of 1.521.521.52 , into water, having a refractive index of 1.331.331.33 ? The critical angle for this interface is closest to which one of the following angles?

A flashlight beam makes an angle of 60° with the plane of the surface of a calm lake before it enters the water. In the water what angle does the beam make with the plane of the surface? The Index of refraction of water is 1.33.

A point source of light is positioned 20.0 m20.0 \mathrm {~m}20.0 m below the surface of a lake. What is the diameter of the largest circle on the surface of the water through which light can emerge into the air? The index of refraction of water is 1.33.1.33 .1.33.

An optic fiber is made of clear plastic with an index of refraction of 1.501.501.50 . For what range of angles of incidence θ\thetaθ with the lateral surface of the fiber will light remain inside the plastic "guide" if it is surrounded by air?

The critical angle for a substance in air is measured at 53.7∘53.7 ^ { \circ }53.7∘ . If light enters this substance from air at 45.0∘45.0 ^ { \circ }45.0∘ with the normal, at what angle with the normal will it continue to travel?

A beam of light in water (of refractive index of 1.331.331.33 ) enters a glass slab (of refractive index 1.501.501.50 ) at an angle of incidence of 60.0∘60.0 ^ { \circ }60.0∘ . What is the angle of refraction in the glass?

A beam of light in air enters a glass slab with an index of refraction of 1.401.401.40 at an angle of incidence of 30.0∘30.0 ^ { \circ }30.0∘ . What is the angle of refraction?

Lucite has an index of refraction of 1.501.501.50 . What is its critical angle if it is in air?

A thin flashlight beam traveling in air strikes a glass plate at an angle of 52∘52 ^ { \circ }52∘ with the plane of the surface of the plate. If the index of refraction of the glass is 1.41.41.4 , what angle will the beam make with the normal in the glass?

Light enters a substance from air at $30.0 ^ { \circ }$ to the normal. It continues within the substance at $23.0 ^ { \circ }$ to the normal. What is the critical angle for this substance when it is surrounded by air?

Light travels from crown glass, with a refractive index of $1.52$ , into water, having a refractive index of $1.33$ ? The critical angle for this interface is closest to which one of the following angles?

A point source of light is positioned $20.0 \mathrm {~m}$ below the surface of a lake. What is the diameter of the largest circle on the surface of the water through which light can emerge into the air? The index of refraction of water is $1.33 .$

An optic fiber is made of clear plastic with an index of refraction of $1.50$ . For what range of angles of incidence $\theta$ with the lateral surface of the fiber will light remain inside the plastic "guide" if it is surrounded by air?

The critical angle for a substance in air is measured at $53.7 ^ { \circ }$ . If light enters this substance from air at $45.0 ^ { \circ }$ with the normal, at what angle with the normal will it continue to travel?

A beam of light in water (of refractive index of $1.33$ ) enters a glass slab (of refractive index $1.50$ ) at an angle of incidence of $60.0 ^ { \circ }$ . What is the angle of refraction in the glass?

A beam of light in air enters a glass slab with an index of refraction of $1.40$ at an angle of incidence of $30.0 ^ { \circ }$ . What is the angle of refraction?

Lucite has an index of refraction of $1.50$ . What is its critical angle if it is in air?

A thin flashlight beam traveling in air strikes a glass plate at an angle of $52 ^ { \circ }$ with the plane of the surface of the plate. If the index of refraction of the glass is $1.4$ , what angle will the beam make with the normal in the glass?