Samacheer Kalvi 9th Science Light Exercise Solutions

Concave mirrors and concave lenses have negative focal lengths (f < 0) per the Cartesian sign convention. Since the focus lies in front of the mirror (on the same side as the object for a concave mirror), the distance is measured against the direction of incident light, making it negative. Convex mirrors and convex lenses have positive focal lengths because their focus lies behind the reflecting/refracting surface.

Concave mirror is the only spherical mirror that can produce both types of images. (i) When the object is placed between F and P, the concave mirror forms a virtual, erect, and enlarged image. (ii) When the object is placed at C, it forms a real, inverted, and same-sized image. A convex mirror always gives a diminished image and can never produce a same-sized or enlarged real image.

The image is formed at infinity. When the object is at the focus, the reflected rays become parallel and never actually converge, forming a highly magnified image at an infinite distance. This principle is used in torchlights and searchlights where the bulb is placed at the focus to produce a parallel beam of light.

Light bends because its speed changes when moving between media of different optical densities. In a denser medium, light slows down and the wavefront closer to the interface decelerates first, causing the ray to bend towards the normal. In a rarer medium, light speeds up and the ray bends away from the normal. This change in direction is what we call refraction, governed by Snell's law: μ₁ sin i = μ₂ sin r.

The speed of light in vacuum is 3 × 10⁸ m/s (approximately 3 lakh km per second). This is the maximum speed at which light can travel in any medium. In all other transparent media like glass, water, or diamond, light travels slower than this value. The ratio of the speed of light in vacuum to its speed in a medium gives the refractive index of that medium.

A concave mirror focuses light onto a small area and produces a magnified, erect image when the object (teeth) is placed close to it, within its focal length. This allows the dentist to see a clear, enlarged view of the teeth for examination and treatment. The mirror is held close to the teeth so the object is between F and P, producing a virtual, erect, and magnified image.

Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media: μ₁ sin i = μ₂ sin r. For light going from air (μ₁ ≈ 1) into a medium of refractive index μ, this simplifies to μ = sin i / sin r. This constant is the refractive index of the second medium with respect to the first.

A ray of light travelling along the principal axis strikes the mirror normally, so the angle of incidence is 0°. By the law of reflection, the angle of reflection is also 0°, and the ray retraces its path back along the principal axis. This is why a ray directed towards the centre of curvature retraces its path.

A real image is formed by the actual convergence of reflected or refracted rays and can be projected on a screen; it is always inverted. A virtual image is formed by the apparent convergence of rays and cannot be projected on a screen; it is always erect. Concave mirrors can produce both real and virtual images depending on object position, while convex mirrors always produce virtual images.

A concave mirror produces different types of images depending on the object's position relative to the focus (F) and centre of curvature (C). The mirror formula 1/f = 1/v + 1/u and magnification m = –v/u govern all cases.

(i) Object at infinity: Rays arrive parallel to the principal axis. After reflection, they converge at the focus F. The image is real, inverted, and highly diminished (point-sized). This is how distant stars appear at the focus of a concave telescope mirror.

(ii) Object beyond C: Rays from the object converge between F and C after reflection. The image is real, inverted, and diminished. As the object moves farther away, the image shrinks and moves closer to F.

(iii) Object at C: The image forms exactly at C. It is real, inverted, and the same size as the object. This is the only position where object and image are equidistant from the mirror.

(iv) Object between C and F: The reflected rays converge beyond C. The image is real, inverted, and magnified. A projector uses this configuration — the slide (object) is between C and F and the enlarged image is projected on a distant screen.

(v) Object at F: Reflected rays become parallel, meeting at infinity. The image is real, inverted, and highly magnified (formed at infinity). Searchlights place the bulb at F to produce a parallel beam.

(vi) Object between F and P: Reflected rays diverge but appear to come from behind the mirror. The image is virtual, erect, and magnified. This is the configuration used by dentists and in shaving mirrors.

Summary table:

Refraction is the bending of light as it passes from one transparent medium to another due to a change in its speed. When light enters a denser medium, it slows down and bends towards the normal; when it enters a rarer medium, it speeds up and bends away from the normal.

(a) Rarer to denser medium (e.g., air to glass): The ray bends towards the normal. The speed of light decreases because the denser medium offers more resistance to the passage of light. The angle of refraction (r) is smaller than the angle of incidence (i). Practical examples include a coin at the bottom of a pool appearing raised, and a pencil in water appearing bent at the surface.

(b) Denser to rarer medium (e.g., glass to air): The ray bends away from the normal. The speed of light increases as the medium becomes optically less dense. The angle of refraction is larger than the angle of incidence. If the angle of incidence exceeds the critical angle, total internal reflection occurs — the ray reflects entirely back into the denser medium. This is the principle behind optical fibres and diamond brilliance.

(c) Normal incidence (i = 0°): When light hits the interface perpendicular to the surface (along the normal), it passes straight through without any deviation. The direction does not change, though the speed does change in the new medium.

Snell's Law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media:

For light going from air (μ₁ ≈ 1) to a medium with refractive index μ:

where c = speed of light in vacuum, v = speed of light in the medium. Snell's law is fundamental to understanding lenses, prisms, and all optical instruments.

Total internal reflection (TIR) occurs when light travelling from a denser medium to a rarer medium strikes the boundary at an angle of incidence greater than the critical angle. Instead of refracting out, the light is completely reflected back into the denser medium. Two conditions must be satisfied simultaneously: (1) light must travel from a denser medium to a rarer medium, and (2) the angle of incidence must exceed the critical angle for that pair of media.

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly 90°. It is calculated using: sin θc = μ_raer / μ_denser = 1/μ (when the rarer medium is air). For glass (μ = 1.5), θc ≈ 42°; for diamond (μ = 2.41), θc ≈ 24.4°.

Applications of total internal reflection:

• Diamonds: The extremely small critical angle (≈24°) combined with the high refractive index means that most light entering a cut diamond undergoes multiple total internal reflections before emerging, producing its characteristic sparkle.
• Optical fibres: Light signals travel through glass or plastic fibres by repeated TIR, enabling high-speed data transmission over long distances with minimal loss.
• Mirages: On hot days, the air near the ground is much less dense than the air above. Light from the sky undergoes TIR near the ground, creating the illusion of a water pool on the road.
• Prisms in binoculars: Right-angled prisms use TIR to reflect light, allowing compact binocular designs without mirror coatings that would absorb some light.

m = –3 (real image, so negative), u = –7 cm (object in front of mirror) m = –v/u → –3 = –v/(–7) → v = –21 cm Image is formed 21 cm in front of the mirror (real, inverted).

μ = c/v → v = c/μ = 3 × 10⁸ / 1.5 = 2 × 10⁸ ms⁻¹

μ = c/v = 3 × 10⁸ / 2.25 × 10⁸ = 1.33

1/f = 1/v + 1/u → 1/10 = 1/v + 1/(–15) → 1/v = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 v = –30 cm (real image, 30 cm in front of mirror) m = –v/u = –(–30)/(–15) = –2 Image height = m × object height = –2 × 1 = –2 cm (inverted, 2 cm tall)

μ = sin i / sin r = sin 45° / sin 30° = (1/√2) / (1/2) = 2/√2 = √2 = 1.414

v = c/μ = 3 × 10⁸ / 2.41 = 1.245 × 10⁸ m/s