Reflection Quiz 1 (30 MCQs)

Explanations: The correct answer is C) (x, y) $\rightarrow$ (-x, -y). This rule reflects the figure across both axes, moving any point from a positive quadrant to Quadrant III. For example, if a vertex starts at (a, b), where both \(a\) and \(b\) are positive integers, applying this rule will move it to (-a, -b), which is in Quadrant III.

Explanations: Virtual images are typically formed by mirrors and cannot be projected onto a screen, making option A correct. Virtual images are upright (not inverted), which makes B the correct answer since an inverted image would indicate a real image formation. Virtual images can appear of the same size as the object or laterally reversed, depending on the situation, so C and D could potentially apply.

Explanations: Reflection is the correct term used to describe light as it strikes a smooth, shiny surface and bounces off. This phenomenon occurs when light waves hit a reflective surface and are redirected back into their original medium or another medium in a predictable manner.

Explanations: Irregular reflection occurs when light bounces off a surface that is not smooth, leading to scattered reflections in various directions. Uneven ground (Option B) fits this description perfectly as it provides an irregular surface for light to reflect off of.

Explanations: Smooth glass surfaces reflect light the best because they have a highly polished and uniform surface, minimizing irregularities that would cause light to scatter. This results in a higher degree of specular reflection, where light bounces off at the same angle it hits the surface.

Explanations: Reflection preserves distance between points, angle measurement, and shape. However, orientation is not preserved because a reflection flips the figure over a line, reversing its direction.

Explanations: The water in the tank would move forward due to inertia. When the brakes are applied, the tank comes to a stop, but the water continues moving with its initial velocity because it has inertia. This causes the water to move forward relative to the stationary tank.

Explanations: Reflection is the bouncing of light off an object, where the light ray changes direction and moves back into the same medium or a different one at an angle equal to the angle of incidence.

Explanations: Refraction is the bending of light as it passes from one medium to another with a different density, causing the light's path to change direction. This phenomenon explains why light appears bent when passing through a glass prism or entering water at an angle.

Explanations: The angle of incidence is the angle between the incident ray and the normal to the reflecting surface, which is perpendicular to the surface. Therefore, if the angle of incidence is 45 degrees, the angle between the incident ray and the reflecting surface would be 90 degrees minus the angle of incidence, i.e., 90 - 45 = 45 degrees.

Explanations: Pinhole camera (Option B) is a device that can be used to image the sun. It works by allowing light from the sun to pass through a small hole, creating an inverted image on a screen placed opposite the hole. This method does not require lenses and can safely project the image of the sun without direct exposure.

Explanations: Diffuse reflection occurs when light is reflected from a surface in many different directions, which happens on rough surfaces where the light bounces off at various angles due to the unevenness of the surface. A rough wall fits this description perfectly as it causes light to scatter in multiple directions.

Explanations: The translation \( T(7, 8) \) means that every point in the plane is moved 7 units to the right and 8 units up. For the point \( K(-6, -2) \), applying this translation involves adding 7 to the x-coordinate and 8 to the y-coordinate. Step-by-step: 1. Original coordinates of \( K \): \( (-6, -2) \) 2. New x-coordinate: \( -6 + 7 = 1 \) 3. New y-coordinate: \( -2 + 8 = 6 \) Thus, the image of \( K(-6, -2) \) after translation \( T(7, 8) \) is \( (1, 6) \).

Explanations: The velocity of light in vacuum is a fundamental constant in physics, denoted as \(c\), and its value is approximately \(3 \times 10^8\) meters per second (m/s). This value aligns with Option D.

Explanations: The correct answer is C) -15 cm. The negative sign indicates that the image formed by a concave mirror is inverted, and the magnification formula \(m = \frac{h_i}{h_o} = -\frac{v}{u}\) can be used to find the size of the image. Given \(u = -20\) cm (since the object is on the left side of the mirror), and knowing that the focal length \(f = -15\) cm, we use the mirror formula \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) to find \(v\). Solving this gives us \(v = 60\) cm. The magnification \(m = \frac{h_i}{h_o} = -\frac{v}{u} = -\frac{60}{-20} = 3\), so the image size is \(5 \times 3 = 15\) cm, with a negative sign indicating it's inverted.

Explanations: The magnification produced by a convex mirror is always positive because the image formed by a convex mirror is always virtual and erect. This means that the image does not actually exist in front of the mirror, but appears to be behind it, and is upright relative to the object.

Explanations: When a point is reflected over the x-axis, its x-coordinate remains unchanged while its y-coordinate changes sign (it becomes negative).

Explanations: When an incident ray passes through the focal point (F) and hits a concave mirror, it will reflect parallel to the principal axis of the mirror. This is a fundamental property of concave mirrors and can be observed in various optical devices like telescopes.

Explanations: When a point is reflected across the y-axis, its x-coordinate changes sign while the y-coordinate remains the same. For the ordered pair (-3, 4), reflecting it across the y-axis results in (3, 4).

Explanations: The claimed correct answer is A) 0.8 m. This can be determined by understanding the initial and final positions of the ladder using the Pythagorean theorem. Initially, with a 5m ladder reaching 4m up the wall, we have: \[ \text{Base}^2 + \text{Height}^2 = \text{Hypotenuse}^2 \] \[ \text{Base}^2 + 4^2 = 5^2 \] \[ \text{Base}^2 + 16 = 25 \] \[ \text{Base}^2 = 9 \] \[ \text{Base} = 3 \, \text{m} \] When the foot of the ladder is moved 1.6 m closer to the wall: \[ \text{New Base} = 3 - 1.6 = 1.4 \, \text{m} \] Using the Pythagorean theorem again for the new position: \[ 5^2 = 1.4^2 + \text{Height}^2 \] \[ 25 = 1.96 + \text{Height}^2 \] \[ \text{Height}^2 = 23.04 \] \[ \text{Height} = \sqrt{23.04} \approx 4.8 \, \text{m} \] The distance by which the top of the ladder slides upwards is: \[ 4.8 - 4 = 0.8 \, \text{m} \]

Explanations: The new figure created from a transformation is the image of the original figure, which has the same size and shape as the preimage but may be in a different position due to reflection, rotation, translation, or dilation.

Explanations: Reflection is the bouncing of light from a surface, where the light ray bounces off at an angle equal to the angle it approached (angle of incidence equals angle of reflection). This phenomenon explains how mirrors work and why objects appear in reflective surfaces.

Explanations: When reflecting a point across the x-axis, the x-coordinate remains unchanged while the y-coordinate is multiplied by -1. For point P with coordinates (-8, -2), after reflection, its new coordinates will be (-8, 2).

Explanations: A 270$^\circ$ counterclockwise rotation will result in the same image as a 90$^\circ$ clockwise rotation because both transformations effectively rotate the object by the same angle, just in opposite directions. A full circle is 360$^\circ$, so a 270$^\circ$ counterclockwise rotation means rotating three-quarters of the way around the circle.

Explanations: The Law of Reflection states that the angle at which light (or any wave) hits a surface (angle of incidence) is equal to the angle at which it bounces off (angle of reflection). This principle applies universally for all types of waves, including sound and water waves.

Explanations: When an incident ray passes through the focus of a parabolic mirror, it reflects off the surface and becomes parallel to the principal axis. This is a fundamental property of parabolic reflectors used in various optical devices like satellite dishes or headlights.

Explanations: Polished metal has a smooth surface that minimizes light absorption and maximizes reflection, making it the best reflector among the options provided.

Explanations: The area of a figure after dilation is scaled by the square of the scale factor. Since the scale factor here is 3, the new area \( A' \) will be \( 3^2 \times A = 9A \). Therefore, option D correctly represents this relationship.

Explanations: Reflection involves flipping a point over a line, typically the x-axis or y-axis. The correct algebraic representation for reflecting a point (x, y) over the x-axis is (x, -y), and over the y-axis is (-x, y). Option B represents a translation, not a reflection.

Explanations: A convex mirror always forms a diminished image irrespective of the position of the object in front of it because its reflective surface curves outward, causing light rays to diverge before reaching the mirror. This results in an upright and smaller virtual image.