Ans: Laws of Reflection: (1) The angle of incidence equals the angle of reflection (∠i = ∠r). (2) The incident ray, reflected ray, and normal to the surface at the point of incidence all lie in the same plane. Image in a plane mirror: Virtual (cannot be projected on screen), Erect (upright), Laterally inverted (left-right reversed), Same size as object, Located as far behind the mirror as the object is in front. Example: when you raise your right hand, your mirror image appears to raise its left hand.

Ans: Refraction is the bending of light when it passes from one transparent medium to another due to change in speed. Light bends toward the normal when entering a denser medium (speed decreases); bends away from normal entering a rarer medium (speed increases). Snell's Law: n₁sinθ₁ = n₂sinθ₂. Refractive index n = speed of light in vacuum / speed in medium. Pencil in water: light from the submerged part of the pencil travels from water (denser) to air (rarer), bending away from normal as it exits. The observer's eye traces the light back in a straight line, perceiving the pencil's submerged part at a different position — the pencil appears bent at the water surface.

Ans: Concave mirror (converges light): Used as shaving/makeup mirrors (produces magnified, erect, virtual image when object is close). Used in torches, vehicle headlights, solar cookers (as reflectors). Used by dentists to see enlarged image of teeth. Used in large reflecting telescopes. Convex mirror (diverges light): Used as rear-view mirrors in vehicles — gives a wider field of view and always produces erect, diminished, virtual images. Used in shops as security mirrors (wide coverage area). Note: Convex mirrors always show diminished images, making objects appear farther than they are.

Ans: Myopia (nearsightedness): near objects seen clearly, distant objects blurry. Cause: eyeball too long or lens too curved; image forms in front of retina. Correction: concave (diverging) lens. Hypermetropia (farsightedness): far objects seen clearly, near objects blurry. Cause: eyeball too short or lens too flat; image forms behind retina. Correction: convex (converging) lens. Presbyopia: age-related loss of near vision; eye lens becomes rigid, loses flexibility. Correction: bifocal lenses. Astigmatism: uneven curvature of cornea; blurred vision at all distances. Correction: cylindrical lenses. The near point of a normal human eye is 25 cm; far point is infinity.

Ans: Sky appears blue: When sunlight enters the atmosphere, air molecules scatter shorter wavelengths (blue, violet) more than longer wavelengths (Rayleigh scattering). Blue light is scattered in all directions, making the sky look blue. (Violet is scattered even more, but our eyes are less sensitive to violet.) Sunrise/sunset: The sun is near the horizon, so sunlight travels through a much thicker layer of atmosphere. Blue light is scattered away, leaving mainly red and orange light (longer wavelengths, less scattered) to reach our eyes — making the sun appear red/orange.

Ans: It is the point on the principal axis where rays parallel to the principal axis meet after reflection from the concave mirror.

Ans: Dioptre (D), where 1 D = 1 m⁻¹.

Ans: A convex mirror, because it gives an erect, diminished image and a wide field of view.

Ans: At the centre of curvature (C) of the mirror. The image is formed at C, real and inverted.

Ans: It means the speed of light in diamond is 1/2.42 times its speed in vacuum, so light travels about 2.42 times slower in diamond than in vacuum.

Ans: Light travels faster in water. Since n = c/v, speed v = c/n. In water v = 3 × 10⁸/1.33 ≈ 2.26 × 10⁸ m/s; in glass v = 3 × 10⁸/1.5 = 2 × 10⁸ m/s. A lower refractive index means a higher speed.

Ans: Starlight undergoes atmospheric refraction in layers of varying density, so its apparent position and brightness keep changing; a star is a point source, so it twinkles. A planet is nearer and acts as an extended source; the variations from the many points average out, so it does not twinkle.

Ans: f = −15 cm, v = −10 cm. 1/u = 1/v − 1/f = −1/10 + 1/15 = −1/30, so u = −30 cm. Magnification m = v/u = (−10)/(−30) = +1/3 ≈ +0.33. The image is virtual, erect and diminished.

Ans: f = 1/P = 1/(−2) = −0.5 m = −50 cm. A negative focal length means it is a concave (diverging) lens.

Ans: u = −25 cm, f = −15 cm. 1/v = 1/f − 1/u = −1/15 + 1/25 = −2/75, so v = −37.5 cm. m = −v/u = −(−37.5)/(−25) = −1.5. Image size h' = m × h = −1.5 × 4 = −6 cm. The image is formed 37.5 cm in front of the mirror, real, inverted and enlarged (6 cm).

Ans: Myopia (near-sightedness) is a defect in which a person can see near objects clearly but not distant objects. Causes: the eyeball is too long, or the eye lens is too thick (excessive curvature, short focal length), so the image forms in front of the retina. Correction: a concave lens of suitable power, which diverges the rays so that the image falls on the retina.

Ans: Due to atmospheric refraction. Light from the Sun just below the horizon bends towards the normal as it enters the denser layers of the atmosphere, so the apparent position of the Sun is slightly higher than the actual position. We therefore see the Sun about 2 minutes before it actually rises, and for about 2 minutes after it sets.

Ans: u = −15 cm, f = +10 cm. 1/v = 1/f + 1/u = 1/10 − 1/15 = 1/30, so v = +30 cm. m = v/u = 30/(−15) = −2. The image is real, inverted and enlarged (twice the size), formed 30 cm on the other side of the lens.

Ans: (a) At infinity: image at F, highly diminished, real, inverted. (b) Beyond C: between F and C, diminished, real, inverted. (c) At C: at C, same size, real, inverted. (d) Between C and F: beyond C, enlarged, real, inverted. (e) Between F and P: behind the mirror, enlarged, virtual, erect.

Ans: Laws of refraction: (1) The incident ray, refracted ray and normal at the point of incidence lie in the same plane. (2) For light passing between two given media, the ratio sin i / sin r is a constant (Snell's law). Refractive index n is the ratio of the speed of light in vacuum to its speed in the medium: n = c/v. For glass, n = 3 × 10⁸ ÷ 2 × 10⁸ = 1.5.