Question 1

A person jogs toward a plane mirror at a speed of 3 m/s. How fast is he approaching his image in the mirror?

Accepted Answer

When a person moves towards a plane mirror at a speed of 3 m/s, the image in the mirror also moves towards the person at the same speed. Therefore, they are approaching each other at a combined speed of 6 m/s.

Question 2

An object that is 3.4 mm tall is placed 25 cm from the vertex of a convex spherical mirror. The radius of curvature of the mirror has magnitude 73 cm.
(a)How far is the image from the vertex of the mirror?
(b)What is the height of the image?

Accepted Answer

The answer of An object that is 3.4 mm tall...

Question 3

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

Accepted Answer

The critical angle is given by the formula:

θc = sin^-1(1/n)

where n is the refractive index of the denser medium (in this case, lucite) with respect to the rarer medium (in this case, air).

Plugging in the values, we get:

θc = sin^-1(1/1.50) = 41.8°

Therefore, the correct choice is C.

Question 4

An object that is 4.0 cm tall is placed 15 cm in front of a concave mirror of focal length 20 cm.
(a)Where is the image formed and how far is it from the mirror?
(b)How tall is the image?

Accepted Answer

The answer of An object that is 4.0 cm tall...

Question 5

David stands 2.5 m in front of a plane mirror.
(a)How far from David is his image in the mirror?
(b)If David moves away from the mirror at 1.5 m/s, how fast are David and his image moving apart from each other?
(c)If David is 180 cm tall, how tall is his image in the mirror?

Accepted Answer

The answer of David stands 2.5 m in front of...

Question 6

A stature that is 3.0 cm tall statue is 24 cm in front of a concave mirror. The magnitude of the radius of curvature of the mirror is 20 cm.
(a)Is the image real or virtual?
(b)How far is the image from the mirror?
(c)Is the image upright or inverted?
(d)How tall is the image?

Accepted Answer

The answer of A stature that is 3.0 cm tall...

Question 7

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

Accepted Answer

The answer of An optic fiber is made of clear...

Question 8

A laser beam strikes a plane mirror's reflecting surface with an angle of incidence of 43°. What is the angle between the incident ray and the reflected ray?

Accepted Answer

The angle of incidence is equal to the angle of reflection, so the angle between the incident ray and the reflected ray is 43°+43°=86°.

Question 9

A scuba diver is 1.2 m beneath the surface of a still pond of water. At what angle relative to the normal at the surface must the diver shine a beam of light toward the surface in order for a person on a distant bank to be able to see it? The index of refraction for water is 1.33.

Accepted Answer

The answer of A scuba diver is 1.2 m beneath...

Question 10

The speed of light in a material is $0.41 \mathrm { c }$ What is the critical angle of a light ray at the interface between the material and a vacuum?

Accepted Answer

The critical angle can be calculated using the formula $\theta_c = \sin^{-1}(\frac{n_2}{n_1})$, where $n_1$ is the refractive index of the material and $n_2$ is the refractive index of the vacuum (1). The refractive index $n_1$ is the ratio of the speed of light in vacuum to the speed of light in the material, which is $\frac{1}{0.41}$. Calculating $\theta_c$ gives approximately 24°.

Question 11

During the investigation of a new type of optical fiber having an index of refraction $n = 1.21 )$ a laser beam is aimed at the flat end of a straight fiber, as shown in the figure. What is the maximum angle of incidence ?₁ if the beam is not to escape from the sides of the fiber if it is surrounded by air?

Accepted Answer

The answer of During the investigation of a new type...

Question 12

Two plane mirrors make an angle of $30 ^ { \circ }$ with each other. A light ray enters the system and is reflected once off of each mirror. Through what angle is the ray turned?

Accepted Answer

The ray is reflected at 30° from the first mirror and then at 30° from the second mirror, for a total of 60°.

Question 13

A tank holds a layer of oil, of thickness T_o = 1.43 m, that floats on a layer of syrup of thickness T_s = 0.640 m, as shown in the figure. Both liquids are clear and do not mix together. A light ray, originating at the bottom of the tank at point P, crosses the oil-syrup interface at a point 0.900 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m to the right of P and at the critical angle. What is the index of refraction of the oil?

Accepted Answer

The answer of A tank holds a layer of oil,...

Question 14

A glass plate having an index of refraction is 1.66 is immersed in a certain alcohol. The surface of the glass is inclined at an angle of 44° with the vertical. When a horizontal ray in the glass strikes the interface, you observe that it is at the critical angle. What is the index of refraction of the alcohol?

Accepted Answer

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

Question 15

An object 2.0 cm tall is placed 24 cm in front of a convex mirror having a focal length of magnitude 30 cm.
(a)Where is the image formed and how far is it from the mirror?
(b)How tall is the image?

Accepted Answer

The answer of An object 2.0 cm tall is placed...

Question 16

A light beam is traveling inside a glass block that has an index of refraction of 1.46. As this light arrives at the surface of the block, it makes an angle of 53.0° with the normal. At what angle with the normal in the air will it leave the block?

Accepted Answer

The answer of A light beam is traveling inside a...

Question 17

An object that is 75 cm tall is located 3.8 m in front of a plane mirror. The image formed by the mirror appears to be

Accepted Answer

The image formed by a plane mirror appears to be the same distance behind the mirror as the object is in front of it. Therefore, if the object is 3.8 m in front of the mirror, the image appears to be 3.8 m behind the mirror's surface.

Question 18

A tank holds a layer of oil, of thickness T_o = 1.65 m, that floats on a layer of syrup of thickness T_s = 0.830 m, as shown in the figure. Both liquids are clear and do not mix together. A light ray, originating at the bottom of the tank at point P, crosses the oil-syrup interface at a point 0.900 m from the axis. The ray continues and arrives at the oil-air interface, 2.00 m to the right of P and at the critical angle. What is the index of refraction of the syrup?

Accepted Answer

The answer of A tank holds a layer of oil,...

Question 19

A statue that is 2.3 cm tall is placed 15 cm in front of a convex mirror. The magnitude of the radius of curvature of the mirror is 18 cm.
(a)Is the image real or virtual?
(b)How far is the image from the mirror?
(c)Is the image upright or inverted?
(d)How tall is the image?

Accepted Answer

The answer of A statue that is 2.3 cm tall...

Question 20

A ray of light in glass strikes a water-glass interface at an angle of incidence equal to one-half the critical angle for that interface. The index of refraction for water is 1.33, and for the glass it is 1.43. What angle does the refracted ray in the water make with the normal?

Accepted Answer

The critical angle for the interface can be found using:
sin(critical angle) = n₂/n₁
where n₁ is the refractive index of the first medium (glass) and n₂ is the refractive index of the second medium (water). 
sin(critical angle) = 1.43/1.33
critical angle = sin⁻¹(1.43/1.33) = 51.6°

The angle of incidence for the ray of light is half of the critical angle, so θ = (1/2) × 51.6° = 25.8°.

Using Snell's law, the angle of refraction in water can be found:
n₁sinθ = n₂sinϕ
1.43sin(25.8°) = 1.33sinϕ
sinϕ = (1.43/1.33)sin(25.8°)
sinϕ = 0.833
ϕ = sin⁻¹(0.833) = 37°

Therefore, the refracted ray in water makes an angle of 37° with the normal.

Quiz 18: Ray Optics

A person jogs toward a plane mirror at a speed of 3 m/s. How fast is he approaching his image in the mirror?

An object that is 3.4 mm tall is placed 25 cm from the vertex of a convex spherical mirror. The radius of curvature of the mirror has magnitude 73 cm. (a)How far is the image from the vertex of the mirror? (b)What is the height of the image?

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

An object that is 4.0 cm tall is placed 15 cm in front of a concave mirror of focal length 20 cm. (a)Where is the image formed and how far is it from the mirror? (b)How tall is the image?

David stands 2.5 m in front of a plane mirror. (a)How far from David is his image in the mirror? (b)If David moves away from the mirror at 1.5 m/s, how fast are David and his image moving apart from each other? (c)If David is 180 cm tall, how tall is his image in the mirror?

A stature that is 3.0 cm tall statue is 24 cm in front of a concave mirror. The magnitude of the radius of curvature of the mirror is 20 cm. (a)Is the image real or virtual? (b)How far is the image from the mirror? (c)Is the image upright or inverted? (d)How tall is the image?

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

A laser beam strikes a plane mirror's reflecting surface with an angle of incidence of 43°. What is the angle between the incident ray and the reflected ray?

A scuba diver is 1.2 m beneath the surface of a still pond of water. At what angle relative to the normal at the surface must the diver shine a beam of light toward the surface in order for a person on a distant bank to be able to see it? The index of refraction for water is 1.33.

The speed of light in a material is 0.41c0.41 \mathrm { c }0.41c What is the critical angle of a light ray at the interface between the material and a vacuum?

Two plane mirrors make an angle of 30∘30 ^ { \circ }30∘ with each other. A light ray enters the system and is reflected once off of each mirror. Through what angle is the ray turned?

An object 2.0 cm tall is placed 24 cm in front of a convex mirror having a focal length of magnitude 30 cm. (a)Where is the image formed and how far is it from the mirror? (b)How tall is the image?

A light beam is traveling inside a glass block that has an index of refraction of 1.46. As this light arrives at the surface of the block, it makes an angle of 53.0° with the normal. At what angle with the normal in the air will it leave the block?

An object that is 75 cm tall is located 3.8 m in front of a plane mirror. The image formed by the mirror appears to be

A statue that is 2.3 cm tall is placed 15 cm in front of a convex mirror. The magnitude of the radius of curvature of the mirror is 18 cm. (a)Is the image real or virtual? (b)How far is the image from the mirror? (c)Is the image upright or inverted? (d)How tall is the image?

A ray of light in glass strikes a water-glass interface at an angle of incidence equal to one-half the critical angle for that interface. The index of refraction for water is 1.33, and for the glass it is 1.43. What angle does the refracted ray in the water make with the normal?

The speed of light in a material is $0.41 \mathrm { c }$ What is the critical angle of a light ray at the interface between the material and a vacuum?

Two plane mirrors make an angle of $30 ^ { \circ }$ with each other. A light ray enters the system and is reflected once off of each mirror. Through what angle is the ray turned?