Question 1

Thin lenses: A convex lens has a focal length f. An object is placed at a distance between f and 2f on a line perpendicular to the center of the lens. The image formed is located at what distance from the lens?

Accepted Answer

When an object is placed between f and 2f from a convex lens, the image formed is real, inverted, and located farther than 2f from the lens.

Question 2

Thin lenses: Which statements are true about a VIRTUAL image? (There may be more than one correct choice.)

Accepted Answer

C, D, E

Question 3

Refracting telescope: A simple refracting telescope provides large magnification by employing

Accepted Answer

A refracting telescope works by bending light through a lens. The larger the lens, the more light can be collected and the greater the magnification of the image. However, a larger lens also has a longer focal length, which can make it difficult to achieve a high magnification without a long and unwieldy telescope. By using a long focal length objective lens and a short focal length eyepiece, a simple refracting telescope can achieve a large magnification without needing an excessively long or heavy telescope. Choice C is the best option because it employs a long focal length objective lens and a short focal length eyepiece.

Question 4

Snell's law: In the figure, a laser positioned on a ship is used to communicate with a small two-man research submarine resting on the bottom of a lake. The laser is positioned 12 m above the surface of the water, and it strikes the water 20 m from the side of the ship. The water is 76 m deep and has an index of refraction of 1.33. How far horizontally is the submarine from the side of the ship?

Accepted Answer

The answer of Snell's law: In the figure, a laser...

Question 5

Snell's law: Light strikes a 5.0-cm thick sheet of glass at an angle of incidence in air of 50°. The sheet has parallel faces and the glass has an index of refraction 1.50.
(a) What is the angle of refraction in the glass?
(b) After traveling through the glass the light re-emerges into the air. What is the final angle of refraction in air?
(c) As it leaves the glass, by what distance is the path of the ray is displaced from what it was before entering the glass?

Accepted Answer

The answer of Snell's law: Light strikes a 5.0-cm thick...

Question 6

Snell's law: A tank holds a 1.44-m thick layer of oil that floats on a 0.96-m thick layer of brine. Both liquids are clear and do not intermix. Point O is at the bottom of the tank, on a vertical axis. The indices of refraction of the oil and the brine are 1.40 and 1.52, respectively. A ray originating at O crosses the brine-oil interface at a point 0.60 m from the axis. The ray continues and emerges into the air above the oil. What is the angle that the ray in the air makes with the vertical?

Accepted Answer

Using Snell's law, we can find the angle of refraction at the oil-brine interface:
$n_1\sin	heta_1=n_2\sin	heta_2$
where $n_1$ and $n_2$ are the indices of refraction of the two mediums and $	heta_1$ and $	heta_2$ are the angles of incidence and refraction relative to the normal.
At the brine-oil interface, we have:
$n_{brine}\sin	heta_1=n_{oil}\sin	heta_2$
Plugging in the given values:
$1.52\sin	heta_1=1.40\sin	heta_2$
We also know that the ray crosses this interface 0.60 m from the axis, which means that $	heta_1$ and $	heta_2$ must be related by:
$	heta_2=	heta_1+\alpha$
where $\alpha$ is the angle of incidence at the oil-air interface. Using Snell's law again, we have:
$n_{oil}\sin	heta_2=n_{air}\sin\alpha$
Plugging in the given values:
$1.40\sin(	heta_1+\alpha)=1.00\sin\alpha$
Expanding the sine:
$1.40\sin	heta_1\cos\alpha+1.40\cos	heta_1\sin\alpha=1.00\sin\alpha$
We can use the first equation we derived to eliminate $\sin	heta_1$:
$1.52\frac{1.40}{1.52}\cos\alpha+1.40\cos	heta_1\frac{1.40}{1.52}=1.00$
Simplifying:
$\cos\alpha+0.809\cos	heta_1=0.658$
We know that $	heta_1$ must be acute since the ray is traveling away from the axis. Furthermore, if $	heta_1$ were close to 90°, then $	heta_2$ would be close to 90° as well and the ray would not emerge into the air. Therefore, we can make the approximation $\cos	heta_1\approx 1$ (i.e. $	heta_1\approx 0$) and solve for $\cos\alpha$:
$\cos\alpha+0.809\approx 0.658$
$\cos\alpha\approx -0.151$
Since $\alpha$ is acute as well, we must have:
$\alpha\approx 104^\circ$
Finally, the ray in the air makes an angle of $	heta_2+\alpha$ with the vertical line, so we have:
$	heta_2+\alpha\approx 54^\circ$

Question 7

Snell's law: Light in air is initially traveling parallel to the face AC of an equilateral triangular prism, as shown in the figure. The prism is made of glass with an index of refraction of 1.52. If the light does not strike the face AC, what is the angle between the ray as it leaves the prism at face BC and the normal in air at that face?

Accepted Answer

The answer of Snell's law: Light in air is initially...

Question 8

Plane mirrors: As you walk away from a vertical plane mirror, your image in the mirror

Accepted Answer

The image in a plane mirror is always the same height as the object in front of it, regardless of the distance between the mirror and the observer.

Question 9

Compound microscope: Which one of the following is a characteristic of a compound microscope?

Accepted Answer

A compound microscope has a real image formed by the objective lens, which is then magnified by the eyepiece lens. The objective lens is converging, and the eyepiece lens is also converging. Therefore, choices A and B are incorrect. The final image formed by a compound microscope is virtual, as it appears to be located behind the microscope. Therefore, choice C is incorrect, and choice D is also incorrect.

Question 10

Snell's law: A ray of light goes from one transparent material into another, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

Accepted Answer

The answer of Snell's law: A ray of light goes...

Question 11

Thin lenses: A convex lens has focal length f. If an object is located extremely far from the lens (at infinity), the image formed is located what distance from the lens?

Accepted Answer

When an object is located at infinity, a convex lens forms the image at its focal point, which is a distance $f$ from the lens.

Question 12

Snell's law: An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for the oil is 1.15, and for water it is 1.33.)

Accepted Answer

To find the angle of refraction in the water, we first use Snell's law to find the angle of refraction in the oil, then use it again to find the angle in the water. Snell's law is $n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$, where $n_1$ and $n_2$ are the indices of refraction, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, respectively. For air to oil, $n_1 = 1$ (for air), $n_2 = 1.15$ (for oil), and $\theta_1 = 45^\circ$. Solving for $\theta_2$ gives the angle of refraction in the oil. Then, using this angle as the angle of incidence from oil to water, with $n_1 = 1.15$ and $n_2 = 1.33$, we find the angle of refraction in the water, which is approximately 32°.

Question 13

Thin lenses: An object is placed in front of a lens which forms an image of the object.

Accepted Answer

If the image is real, it must be inverted according to the rules of thin lenses.

Question 14

Index of refraction: When light goes from one material into another material having a HIGHER index of refraction,

Accepted Answer

When light goes from one material into another material having a higher index of refraction, its speed decreases due to the slower propagation in the denser material. The wavelength also decreases because the frequency of the light cannot change, and since the speed of light is decreasing, the wavelength must also decrease in order to keep the frequency constant. However, the frequency of the light remains the same. Therefore, option B is the best choice.

Question 15

Spherical mirrors: Suppose you place your face in front of a concave mirror. Which one of the following statements is correct?

Accepted Answer

If you position yourself between the center of curvature and the focal point of the mirror, the image formed will be virtual and enlarged. Therefore, you will not be able to see a sharp image of your face. The other statements are not true in general for all positions in front of a concave mirror.

Question 16

Polarization: Which one of the following is an accurate statement about light?

Accepted Answer

When light strikes a surface at Brewster's angle, only the reflected light is 100% polarized. This means that the reflected light is fully linearly polarized, with the electric field vector perpendicular to the plane of incidence. The transmitted light is not necessarily polarized, but can also be partially polarized or unpolarized, depending on the angle of incidence and the properties of the surface.

Question 17

Thin lenses: A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens?

Accepted Answer

According to the thin lens equation, 1/f = 1/d_o + 1/d_i, where f is the focal length, d_o is the object distance, and d_i is the image distance. If the object is between infinity and 2f, then d_o is positive and greater than infinity. Plugging these values into the thin lens equation and solving for d_i, we get:

1/f = 1/d_o + 1/d_i
1/f - 1/d_o = 1/d_i
d_i = f*d_o / (d_o - f)

Since d_o > f, the denominator (d_o - f) is positive, which means d_i is also positive. Therefore, the image is located on the same side of the lens as the object, and the distance from the lens is less than d_o (i.e. between the lens and the object). If we plug in d_o = 2f, we get:

d_i = f*d_o / (d_o - f) = f*(2f) / (2f - f) = 2f

So the image is located 2f away from the lens. The correct choice is C: between f and 2f.

Question 18

Total internal reflection: The speed of light in a material is  What is the critical angle of a light ray at the interface between the material and a vacuum?

Accepted Answer

The answer of Total internal reflection: The speed of light...

Question 19

Total internal reflection: A ray of light strikes a boundary between two transparent materials, and there is no transmitted ray, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

Accepted Answer

The answer of Total internal reflection: A ray of light...

Question 20

Snell's law: A ray of light passes from glass into a liquid, as shown in the figure. What is the speed of the light in the liquid? (c = 3.00 × 10⁸ m/s)

Accepted Answer

The answer of Snell's law: A ray of light passes...

Quiz 27: Magnetic Field and Magnetic Forces

Thin lenses: A convex lens has a focal length f. An object is placed at a distance between f and 2f on a line perpendicular to the center of the lens. The image formed is located at what distance from the lens?

Thin lenses: Which statements are true about a VIRTUAL image? (There may be more than one correct choice.)

Refracting telescope: A simple refracting telescope provides large magnification by employing

Plane mirrors: As you walk away from a vertical plane mirror, your image in the mirror

Compound microscope: Which one of the following is a characteristic of a compound microscope?

Thin lenses: A convex lens has focal length f. If an object is located extremely far from the lens (at infinity) , the image formed is located what distance from the lens?

Thin lenses: An object is placed in front of a lens which forms an image of the object.

Index of refraction: When light goes from one material into another material having a HIGHER index of refraction,

Spherical mirrors: Suppose you place your face in front of a concave mirror. Which one of the following statements is correct?

Polarization: Which one of the following is an accurate statement about light?

Thin lenses: A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens?

Total internal reflection: The speed of light in a material is What is the critical angle of a light ray at the interface between the material and a vacuum?

Snell's law: A ray of light passes from glass into a liquid, as shown in the figure. What is the speed of the light in the liquid? (c = 3.00 × 10⁸ m/s)

Quiz 27: Magnetic Field and Magnetic Forces

Thin lenses: A convex lens has a focal length f. An object is placed at a distance between f and 2f on a line perpendicular to the center of the lens. The image formed is located at what distance from the lens?

Thin lenses: Which statements are true about a VIRTUAL image? (There may be more than one correct choice.)

Refracting telescope: A simple refracting telescope provides large magnification by employing

Plane mirrors: As you walk away from a vertical plane mirror, your image in the mirror

Compound microscope: Which one of the following is a characteristic of a compound microscope?

Snell's law: A ray of light goes from one transparent material into another, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

Thin lenses: A convex lens has focal length f. If an object is located extremely far from the lens (at infinity) , the image formed is located what distance from the lens?

Thin lenses: An object is placed in front of a lens which forms an image of the object.

Index of refraction: When light goes from one material into another material having a HIGHER index of refraction,

Spherical mirrors: Suppose you place your face in front of a concave mirror. Which one of the following statements is correct?

Polarization: Which one of the following is an accurate statement about light?

Thin lenses: A convex lens has a focal length f. An object is placed between infinity and 2f from the lens along a line perpendicular to the center of the lens. The image is located at what distance from the lens?

Total internal reflection: The speed of light in a material is What is the critical angle of a light ray at the interface between the material and a vacuum?

Total internal reflection: A ray of light strikes a boundary between two transparent materials, and there is no transmitted ray, as shown in the figure. What can you conclude about the indices of refraction of these two materials?

Snell's law: A ray of light passes from glass into a liquid, as shown in the figure. What is the speed of the light in the liquid? (c = 3.00 × 108 m/s)

Snell's law: A ray of light passes from glass into a liquid, as shown in the figure. What is the speed of the light in the liquid? (c = 3.00 × 10⁸ m/s)