Daily Olympiad: Science - Light Reflection Refraction [20260719]

Solution

Correct: D

Plane mirrors always form virtual, erect, and laterally inverted images. The image is of the same size as the object and located at the same distance behind the mirror as the object is in front. A virtual image cannot be obtained on a screen, and an erect image is oriented the same way as the object.

Solution

Correct: B

When an object is placed between the pole (P) and the principal focus (F) of a concave mirror, the reflected rays diverge and appear to intersect behind the mirror. This forms a virtual, erect, and magnified image. This property is utilized in shaving mirrors and dentist's mirrors.

Solution

Correct: B

Refraction is the phenomenon where light changes its direction of propagation (bends) as it passes obliquely from one transparent medium to another, due to a change in its speed. Reflection is the bouncing back of light, dispersion is the splitting of light into its constituent colours, and diffraction is the bending of light around obstacles or through small apertures.

Solution

Correct: B

The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v): n = c/v. Therefore, v = c/n. If n = 1.33, then v = c/1.33. This means the speed of light in water is c/1.33, which is 1.33 times slower than its speed in vacuum.

Solution

Correct: B

For a convex lens, when an object is placed at 2F (twice the focal length, which corresponds to the center of curvature equivalent for mirrors), the image is formed at 2F on the other side of the lens. This image is real, inverted, and of the same size as the object.

Solution

Correct: D

Regardless of the object's position (for a real object), a concave lens always produces a virtual, erect, and diminished image. This image is formed between the optical center and the principal focus (F) on the same side of the lens as the object.

Solution

Correct: C

Magnification (m) is given by -v/u for mirrors. A negative sign for magnification indicates that the image is real and inverted. A magnitude of 1 (|m|=1) means the image is of the same size as the object. Thus, m = -1 implies a real, inverted, and same-size image. This specific case occurs when an object is placed at the center of curvature (C) of a concave mirror.

Solution

Correct: A

The power of a lens (P) is the reciprocal of its focal length (f) in meters. P = 1/f(m). Given f = +25 cm, convert it to meters: f = +0.25 m. So, P = 1 / 0.25 = +4 Dioptres (D). The positive sign indicates it is a convex (converging) lens.

Solution

Correct: B

In the New Cartesian Sign Convention, the pole (or optical center for lenses) is taken as the origin. The incident light is generally considered to travel from left to right. Distances measured in the same direction as incident light are taken as positive, while distances measured against the direction of incident light are taken as negative.

Solution

Correct: C

Concave mirrors are used in car headlights. When the light bulb is placed at the principal focus of the concave mirror, it produces a powerful, parallel beam of light, which is essential for illumination during driving. Rear-view and security mirrors use convex mirrors to provide a wider field of view with diminished, erect images.

Solution

Correct: C

For a convex lens to act as a simple microscope (magnifying glass), it must produce a virtual, erect, and magnified image. This occurs when the object is placed between the optical center (O) and the principal focus (F) of the lens.

Solution

Correct: C

When light passes from one transparent medium to another (e.g., from air to glass), its speed changes, causing its wavelength to also change. However, the frequency of light, which is determined by its source, remains constant during refraction. The relationship is given by v = fλ, where v is speed, f is frequency, and λ is wavelength.

Solution

Correct: B

For a concave mirror, according to the New Cartesian Sign Convention, the focal length (f) is negative: f = -10 cm. The object distance (u) is always negative for a real object: u = -15 cm. Using the mirror formula: 1/f = 1/v + 1/u. 1/v = 1/f - 1/u 1/v = 1/(-10) - 1/(-15) 1/v = -1/10 + 1/15 To combine, find a common denominator (30): 1/v = -3/30 + 2/30 1/v = -1/30 v = -30 cm. The negative sign for 'v' indicates that the image is real and formed in front of the mirror.

Solution

Correct: B

For a convex lens, when a real and inverted image is formed, and its size is equal to the object's size, the object must be placed at 2F, and the image is also formed at 2F on the other side of the lens. Since the image distance (v) is 40 cm (positive for real image formed by convex lens), then 2F = 40 cm. Therefore, the focal length F = 40 cm / 2 = 20 cm. Alternatively, using the lens formula: 1/f = 1/v - 1/u. Since the image is real, inverted, and same size, m=-1. For lenses, m = v/u, so -1 = v/u, which means u = -v. Given v = +40 cm, then u = -40 cm. 1/f = 1/40 - 1/(-40) = 1/40 + 1/40 = 2/40 = 1/20. So, f = +20 cm.

Solution

Correct: C

When light rays from the coin travel from water (a denser medium) to air (a rarer medium), they bend away from the normal as they exit the water surface. When these diverged rays reach the observer's eye, the brain traces them back in straight lines, making the coin appear to be at a shallower, raised position. This bending of light is known as refraction.

Solution

Correct: B

A convex mirror always forms a virtual, erect, and diminished image for any real object placed in front of it. Since the image is always smaller than the object, the ratio of image height to object height (magnification) will always be less than 1. Also, since the image is erect, the magnification will be positive.

Solution

Correct: C

This is one of the fundamental rules for ray diagrams of spherical mirrors. Any ray of light travelling parallel to the principal axis of a concave mirror, after reflection, passes through its principal focus (F). This property is used in applications like solar furnaces and car headlights (in reverse).

Solution

Correct: A

A real image is formed by the actual intersection of reflected or refracted light rays. Because the light rays physically converge at the image location, a real image can be projected onto a screen. Real images are always inverted relative to the object. Virtual images, on the other hand, are formed when rays appear to diverge and cannot be obtained on a screen.

Solution

Correct: B

According to the laws of refraction, when light travels from an optically rarer medium (like air) to an optically denser medium (like glass or water), its speed decreases, and it bends towards the normal at the interface between the two media. Conversely, it bends away from the normal when passing from a denser to a rarer medium.

Solution

Correct: B

A positive power (+2.5 D) indicates a converging lens, which is a convex lens. The focal length (f) is the reciprocal of the power (P) in meters: f = 1/P. So, f = 1 / (+2.5) m = 0.4 m. Converting to centimeters, f = 0.4 * 100 cm = +40 cm. The positive focal length also confirms it is a convex lens.