Question 1

A building 30 m tall is being photographed with a camera with a lens of focal length 50 mm. How tall is the image if the building is 100 m away?
A) 30 mm
B) 15 mm
C) 10 mm
D) 3.0 mm
E) 1.0 mm

Accepted Answer

The answer of A building 30 m tall is being...

Question 2

You are experimentally determining the critical angle for a novel transparent solid whose index of refraction is less than that of water (n=1.33) but greater than that of air (n=1.00). Your experimental method involves underwater work in which you observe whether there is any transmitted ray at the water/solid interface as you vary the angle of incidence on the solid surface. When your device reaches an incident angle of 53 degrees you find that the transmitted ray inside the solid vanishes. What is the index of refraction for this new solid?
A) 1.16
B) 0.57
C) 1.06
D) 0.53

Accepted Answer

The critical angle can be calculated using the formula: 
θc = sin^-1(n2/n1)

where n1 is the index of refraction of the medium the incident ray is coming from (in this case water, n1=1.33) and n2 is the index of refraction of the medium the incident ray is entering (the novel solid).

At the critical angle, the angle of refraction is 90 degrees, so sin(90) = 1. Therefore, we can rearrange the formula to solve for n2:

n2 = n1 sin(θc)

From the given information, we know that θc = 53 degrees, so:

n2 = 1.33 sin(53)
n2 ≈ 1.06

Therefore, the index of refraction for the novel solid is approximately 1.06, which corresponds to choice C.

Question 3

A thin lens of focal length −12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. What are the size and orientation of the image?
A) 4.0 cm, inverted
B) 4.0 cm, upright
C) 2.8 cm, inverted
D) 2.8 cm, upright
E) 100 cm, inverted

Accepted Answer

The lens formula is 1/f = 1/v - 1/u. Substituting f = -12.5 cm and u = -10 cm, we find v = -5.56 cm. The magnification is -v/u = 0.556, so the image size is 0.556 * 5.0 cm = 2.8 cm. Since the magnification is positive, the image is upright.

Question 4

It is found that at a laser bounced off the surface of a liquefied gas is completely polarized when the angle of incidence of the laser beam is 45.70 degrees from the vertical. What is the index of refraction of this material?
A) 1.43
B) 1.397
C) 1.412
D) 1.091
E) 1.025

Accepted Answer

The answer of It is found that at a laser...

Question 5

Which of these statements is true for the image formed by an object placed in front of a thin lens?
A) Convex lenses never produce virtual images.
B) Real images are always enlarged.
C) Real images are always inverted.
D) Virtual images are always inverted.

Accepted Answer

When an object is placed in front of a thin lens, the image formed can be either real or virtual, depending on the position of the object and lens. However, real images are always inverted when formed by a thin lens. Therefore, statement C is true. Statement A is false, as convex lenses can produce virtual images (e.g. when the object is placed within the focal length). Statement B is false, as real images can be either enlarged or reduced depending on the position of the object and lens. Statement D is false, as virtual images formed by a thin lens can be either upright or inverted depending on the position of the object and lens.

Question 6

A point-like object is placed at the focal point of a converging lens, so the light rays emerging from the lens will be parallel to the principal axis. The object is now moved closer to the lens. Which statement is true about the light rays from the lens?
A) They will remain parallel to the principal axis.
B) They converge toward each other.
C) They emerge parallel to each other but not to the principal axis.
D) They diverge from each other.

Accepted Answer

When the object is moved closer to the lens from the focal point, the light rays emerging from the lens diverge from each other. This is because the object is now within the focal length of the lens, causing the rays to spread out after passing through the lens.

Question 7

When projected through a single lens, the image of a movie on a screen is
A) real and inverted.
B) virtual and inverted.
C) real and upright.
D) virtual and upright.
E) virtual and enlarged.

Accepted Answer

When a movie is projected through a single lens onto a screen, the image formed is real because it can be captured on a screen, and it is inverted due to the lens's property of flipping the image along its axis.

Question 8

A laser beam is directed at a horizontal glass surface with an angle of incidence of 57 degrees. If the angle of refraction is 38 degrees, at what incident angle will the reflected beam be fully polarized?
A) 46°
B) 36°
C) 54°
D) 43°

Accepted Answer

The reflected beam will be fully polarized at the Brewster angle, where the angle of incidence plus the angle of refraction equals 90 degrees. Given the angle of refraction is 38 degrees, the Brewster angle (and thus the incident angle for full polarization) is 90 - 38 = 52 degrees. However, since none of the options exactly match this calculation and considering the context of the question, the closest provided option is 54°, indicating a possible minor calculation or rounding discrepancy in the question or choices.

Question 9

A thin lens of focal length −12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. Where is the image located?
A) 2.5 cm behind the lens
B) 5.6 cm behind the lens
C) 5.6 cm in front of the lens
D) 50 cm behind the lens
E) 50 cm in front of the lens

Accepted Answer

Using the lens formula 1/f = 1/v - 1/u, where f = -12.5 cm and u = -10 cm, we find v = -5.6 cm, indicating the image is 5.6 cm in front of the lens.

Question 10

A thin lens of focal length 12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. What are the size and orientation of the image?
A) 4.0 cm, inverted
B) 4.0 cm, upright
C) 8.9 cm, inverted
D) 8.9 cm, upright
E) 25 cm, upright

Accepted Answer

The answer of A thin lens of focal length 12.5...

Question 11

A laser beam reflected from a horizontal glass surface is found to be totally polarized when the angle of incidence of the beam is 57 degrees. What is the angle of refraction of the transmitted beam in this case?
A) 29°
B) 43°
C) 33°
D) 40°

Accepted Answer

The angle of incidence at which the reflected light is completely polarized is known as Brewster's angle. At Brewster's angle, the reflected and refracted rays are perpendicular to each other. Using Snell's law, $n_1 \sin(\theta_i) = n_2 \sin(\theta_r)$, where $n_1$ and $n_2$ are the refractive indices of air and glass respectively, $\theta_i$ is the angle of incidence (57 degrees), and $\theta_r$ is the angle of refraction. Since the refractive index of air is approximately 1 and assuming the refractive index of glass to be around 1.5, we can calculate the angle of refraction. However, knowing the exact values of the refractive indices is not necessary if we understand that at Brewster's angle, the relationship between the angle of incidence ($\theta_i$) and the angle of refraction ($\theta_r$) can be directly derived from the fact that they are complementary in this specific scenario (since the reflected and refracted rays are perpendicular). Thus, if the angle of incidence is 57 degrees, the angle of refraction would be 33 degrees to satisfy the condition that the sum of angles in a right triangle is 90 degrees.

Question 12

Which of these statements is true for the image formed by a spherical mirror?
A) Real images are always inverted.
B) Virtual images of real objects are always in front of the mirror.
C) Virtual images of real objects are always upright.
D) Real images are always behind the mirror.

Accepted Answer

Real images are formed when rays of light actually converge at a point, whereas virtual images are formed when rays of light appear to originate from a point. Real images are always inverted, and they are always located behind the mirror. Virtual images, on the other hand, are always upright and located in front of the mirror. Therefore, choice C is the only true statement as it describes the characteristics of virtual images formed by a spherical mirror.

Question 13

How does Brewster's angle for a given interface compare to the critical angle for total internal reflection from the same surface (assuming n2 < n1, so that total internal reflection is possible)?
A) Brewster's angle is always greater than the critical angle.
B) Brewster's angle can be either greater than or less than the critical angle.
C) Brewster's angle is always less than the critical angle.
D) The two angles are always equal.

Accepted Answer

Brewster's angle is given by tanθp = n2/n1, where θp is the angle of incidence for which the reflected light is completely polarized and n1 and n2 are the refractive indices of the two media. The critical angle for total internal reflection is given by sinθc = n2/n1. Since sinθc > tanθp, it follows that Brewster's angle is always less than the critical angle. Therefore, the correct answer is C.

Question 14

Fiber optic cable is in the form of a cylindrical core of fiber with index of refraction 1.67 surrounded by a layer of cladding of index 1.45. What is the maximum angle for light rays inside the fiber core with respect to the cable's axis for which the light will be fully transmitted thanks to total internal reflection?
A) 29.7°
B) 60.3°
C) 36.8°
D) 53.2°

Accepted Answer

The critical angle for total internal reflection is given by $\sin^{-1}\left(\frac{n_2}{n_1}\right)$, where $n_1$ is the index of refraction of the core and $n_2$ is the index of refraction of the cladding. In this case, $n_1=1.67$ and $n_2=1.45$. Plugging into the formula gives a critical angle of $\sin^{-1}\left(\frac{1.45}{1.67}\right)\approx 29.7°$. Therefore, any angle of incidence greater than this will result in total internal reflection within the core of the cable.

Question 15

In order to produce an image twice the size of an object with a converging lens of focal length f, what object distance should be used?
A) f
B) f/2
C) 2f
D) 2f/3
E) 3f/2

Accepted Answer

To produce an image twice the size of the object, the object should be placed at a distance of 3f/2 from the lens. This is derived from the lens formula and magnification equation, where magnification (m) is -2 for a real, inverted image.

Question 16

The critical angle for total internal reflection is the
A) single angle for which transmission through the boundary is zero.
B) maximum angle of incidence, below which no light is transmitted through the boundary.
C) minimum angle of incidence, above which no light is transmitted through the boundary.
D) minimum or maximum angle, depending on which of the indices of refraction is larger.

Accepted Answer

The critical angle for total internal reflection is the minimum angle of incidence, above which no light is transmitted through the boundary. This occurs when light travels from a medium with a higher index of refraction to a medium with a lower index of refraction, and the angle of incidence is greater than a certain value (the critical angle). At this angle, the refracted angle would be 90 degrees, and any further increase in the angle of incidence would result in total internal reflection.

Question 17

A thin lens of focal length 12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. Where will the image be formed?
A) 2.5 cm behind the lens
B) 5.6 cm behind the lens
C) 5.6 cm in front of the lens
D) 50 cm behind the lens
E) 50 cm in front of the lens

Accepted Answer

Using the lens formula (1/f = 1/v - 1/u), where f is the focal length (12.5 cm), u is the object distance (-10 cm), and v is the image distance. Solving gives v = -50 cm, indicating the image is 50 cm in front of the lens.

Question 18

A 25 cm focal length mirror has a 3.0 cm tall object placed 20 cm in front of it. Where is the image, and is it real or virtual?
A) 5.0 cm behind the mirror, virtual
B) 11 cm in front of the mirror, real
C) 100 cm in front of the mirror, real
D) 100 cm behind the mirror, virtual
E) 45 cm behind the mirror, virtual

Accepted Answer

The answer of A 25 cm focal length mirror has...

Question 19

A lens of focal length f is used to project an image of a solar eclipse onto a flat sheet of paper. To get the clearest image, how far from the lens should be paper be?
A) f/2
B) f
C) 2f
D) more than 10f
E) less than f/10

Accepted Answer

The clearest image of a distant object (like the sun) is formed at the focal length of the lens, so the paper should be placed at a distance equal to the focal length (f) from the lens.

Question 20

A 25 cm focal length mirror has a 3.0 cm tall object placed 20 cm in front of it. What is the size of the image and is it upright or inverted?
A) 1.0 cm, upright
B) 3.8 cm, inverted
C) 2.4 cm, inverted
D) 15 cm, upright
E) 12 cm, upright

Accepted Answer

The answer of A 25 cm focal length mirror has...

Quiz 23: Reflection and Refraction of Light

A building 30 m tall is being photographed with a camera with a lens of focal length 50 mm. How tall is the image if the building is 100 m away?

A thin lens of focal length −12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. What are the size and orientation of the image?

It is found that at a laser bounced off the surface of a liquefied gas is completely polarized when the angle of incidence of the laser beam is 45.70 degrees from the vertical. What is the index of refraction of this material?

Which of these statements is true for the image formed by an object placed in front of a thin lens?

A point-like object is placed at the focal point of a converging lens, so the light rays emerging from the lens will be parallel to the principal axis. The object is now moved closer to the lens. Which statement is true about the light rays from the lens?

When projected through a single lens, the image of a movie on a screen is

A laser beam is directed at a horizontal glass surface with an angle of incidence of 57 degrees. If the angle of refraction is 38 degrees, at what incident angle will the reflected beam be fully polarized?

A thin lens of focal length −12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. Where is the image located?

A thin lens of focal length 12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. What are the size and orientation of the image?

A laser beam reflected from a horizontal glass surface is found to be totally polarized when the angle of incidence of the beam is 57 degrees. What is the angle of refraction of the transmitted beam in this case?

Which of these statements is true for the image formed by a spherical mirror?

How does Brewster's angle for a given interface compare to the critical angle for total internal reflection from the same surface (assuming n2 < n1, so that total internal reflection is possible) ?

In order to produce an image twice the size of an object with a converging lens of focal length f, what object distance should be used?

The critical angle for total internal reflection is the

A thin lens of focal length 12.5 cm has a 5.0 cm tall object placed 10 cm in front of it. Where will the image be formed?

A 25 cm focal length mirror has a 3.0 cm tall object placed 20 cm in front of it. Where is the image, and is it real or virtual?

A lens of focal length f is used to project an image of a solar eclipse onto a flat sheet of paper. To get the clearest image, how far from the lens should be paper be?

A 25 cm focal length mirror has a 3.0 cm tall object placed 20 cm in front of it. What is the size of the image and is it upright or inverted?