Light for NDA: reflection, refraction, the eye and optical instruments

Light is one of the richest chapters for NDA GK. The syllabus lists rectilinear propagation, reflection and refraction, spherical mirrors and lenses, and the human eye, and the devices list adds the periscope, telescope and microscope. Questions come from every part: which mirror a dentist uses, why the sky is blue, why stars twinkle, which lens corrects myopia, why a diamond sparkles.

The calculations are small. Converting focal length to power, adding the powers of two lenses, finding the minimum length of a mirror, or counting images between two mirrors takes seconds. The concept questions need exact wording, especially for images (real or virtual, erect or inverted, magnified or diminished).

Typical question types are:

• properties of the image in a plane mirror, and the uses of concave and convex mirrors;
• image position for a concave mirror or convex lens;
• refractive index, apparent depth and atmospheric refraction;
• total internal reflection and its applications;
• lens power in dioptres;
• dispersion, rainbows and scattering;
• defects of vision and their correction;
• the principle of optical instruments.

Nature and propagation of light

Light is an electromagnetic wave. It needs no medium and travels at about 3 × 10⁸ m/s in a vacuum, slower in water and glass. Sunlight takes about 8 minutes 20 seconds to reach the Earth.

In a uniform medium, light travels in straight lines (rectilinear propagation). That is why opaque objects cast shadows, why eclipses happen, and why a pinhole camera forms a real, inverted image.

Reflection and plane mirrors

Laws of reflection: the angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal lie in one plane.

The image in a plane mirror is virtual, erect, the same size as the object, as far behind the mirror as the object is in front, and laterally inverted. That is why "AMBULANCE" is painted in mirror writing on the front of ambulances.

• To see your full image, you need a mirror at least half your height.
• If a mirror moves a distance x away from a fixed object, the image moves 2x.
• Two plane mirrors at an angle θ form (360/θ) − 1 images when 360/θ is even. At 90° you get 3; at 60°, 5 (the kaleidoscope); parallel mirrors give infinitely many.
• A periscope uses two plane mirrors (or right-angled prisms) at 45°, used in submarines and trenches.

Spherical mirrors

For both concave and convex mirrors, the focal length is half the radius of curvature: f = R/2. The mirror formula is 1/v + 1/u = 1/f, with distances measured from the pole.

A convex mirror always forms a virtual, erect, diminished image, whatever the object's position.

Refraction

Light bends when it passes from one medium to another because its speed changes. Going into a denser medium (air to glass) it bends towards the normal; coming out it bends away.

Refractive index n = speed of light in vacuum ÷ speed in the medium. Water is about 1.33, glass about 1.5, diamond about 2.42. Snell's law: n₁ sin i = n₂ sin r.

On refraction the frequency stays the same; the speed and the wavelength change. Colour depends on frequency, so light keeps its colour in water.

Everyday effects:

• A pool or tank looks shallower than it is: apparent depth = real depth ÷ n.
• A pencil in water looks bent at the surface.
• Stars twinkle because of atmospheric refraction: the light passes through layers of air with changing refractive index. Planets, being closer and appearing as small discs, generally do not twinkle.
• The Sun is visible about 2 minutes before actual sunrise and after actual sunset, again due to atmospheric refraction.

Total internal reflection

When light goes from a denser to a rarer medium and the angle of incidence exceeds the critical angle C, no light is refracted: all of it is reflected. The critical angle satisfies sin C = 1/n. For glass (n = 1.5) it is about 42°; for diamond (n = 2.42) about 24°.

• Optical fibres carry light by repeated total internal reflection. They are used in telecommunication and in endoscopes.
• Diamonds sparkle because the small critical angle traps light inside and sends it out through a few faces.
• A mirage on a hot road or desert: air near the ground is hotter and optically rarer, so light from the sky bends and is totally reflected upward, looking like water.
• Right-angled prisms in binoculars and periscopes reflect light more completely than silvered mirrors.

Lenses and power

A convex lens converges light; a concave lens diverges it. The lens formula is 1/v − 1/u = 1/f.

Power P = 1/f, with f in metres; the unit is the dioptre (D). Convex lenses have positive power, concave lenses negative. For lenses in contact, P = P₁ + P₂.

• A convex lens used with the object inside its focal length gives a virtual, erect, magnified image: the magnifying glass.
• Cameras, projectors, microscopes and telescopes use convex lenses; door peepholes use concave ones.
• A convex glass lens placed in water becomes weaker (its focal length increases), because the refractive index of glass relative to water is smaller than relative to air.
• An air bubble in water acts as a diverging lens.

Dispersion and scattering

Dispersion: a prism splits white light into the seven colours, VIBGYOR. Violet bends most and red least, because glass has a higher refractive index for violet. A rainbow forms by refraction, dispersion and internal reflection of sunlight in raindrops; you see it with the Sun behind you. Newton showed that a second prism can recombine the colours into white light.

Scattering: small particles in the air scatter short wavelengths (blue) much more than long ones (red).

• The sky is blue because blue light is scattered most by air molecules.
• The Sun looks red at sunrise and sunset because its light crosses more air and most of the blue is scattered away.
• Clouds are white because their water droplets are large enough to scatter all colours equally.
• To an astronaut above the atmosphere, the sky looks black.
• Danger signals are red because red is scattered least and can be seen from farthest away.

The Indian physicist C V Raman won the 1930 Nobel Prize in Physics for his work on the scattering of light (the Raman effect).

The human eye and its defects

The eye lens is a convex lens that forms a real, inverted image on the retina. The ciliary muscles change the lens's focal length so that we can focus at different distances (accommodation). A normal eye sees clearly from about 25 cm (near point) to infinity (far point). The iris controls the pupil's size. Rods in the retina work in dim light; cones detect colour. Persistence of vision, about 1/16 s, lets a sequence of still frames look like continuous motion in films.

Instruments: a simple microscope is a single convex lens; a compound microscope uses two convex lenses (a short-focus objective and an eyepiece); an astronomical telescope uses two convex lenses with an objective of long focal length and large aperture; binoculars use lenses plus prisms.

Worked NDA-style MCQs

Q1. A lens has a power of −2.5 D. It is:
(a) concave, f = 40 cm (b) convex, f = 40 cm (c) concave, f = 25 cm (d) convex, f = 2.5 m

f = 1/P = −0.4 m. A negative focal length means a concave lens, 40 cm, as used for myopia. Answer: (a).

Q2. A person 1.8 m tall wants to see a full-length image in a plane mirror. The minimum length of mirror needed is:
(a) 1.8 m (b) 0.6 m (c) 3.6 m (d) 0.9 m

Half the height. Answer: (d).

Q3. An object is placed 20 cm in front of a concave mirror of focal length 10 cm. The image is:
(a) virtual, at 20 cm (b) real, magnified, at 40 cm (c) real, inverted, same size, at 20 cm (d) at infinity

The object is at C (R = 20 cm), so the image is at C. Check: 1/v = 1/f − 1/u = −1/10 + 1/20 = −1/20, so v = −20 cm. Answer: (c).

Q4. The refractive index of glass is 1.5. The speed of light in glass is:
(a) 4.5 × 10⁸ m/s (b) 3 × 10⁸ m/s (c) 2 × 10⁸ m/s (d) 1.5 × 10⁸ m/s

v = c/n = 3 × 10⁸/1.5. Answer: (c).

Q5. Lenses of power +2 D and −1.5 D are placed in contact. The combination is:
(a) concave, f = 2 m (b) convex, f = 50 cm (c) concave, f = 0.5 m (d) convex, f = 2 m

P = +0.5 D, positive, so converging; f = 1/0.5 = 2 m. Answer: (d).

Q6. Two plane mirrors are inclined at 60°. The number of images of an object placed between them is:
(a) 6 (b) 5 (c) 3 (d) infinite

360/60 = 6, which is even, so 6 − 1 = 5. Answer: (b).

Common mistakes

• Putting f in centimetres in P = 1/f. Convert to metres first.
• Swapping the myopia and hypermetropia lenses. Myopia (can't see far) needs concave.
• Thinking frequency changes on refraction. Speed and wavelength change; frequency does not.
• Forgetting the two TIR conditions: denser to rarer, and angle greater than critical.
• Saying red is scattered most. Blue is; red is least, which is why it is used for danger.

Practice set

1. The mirror used as a rear-view mirror in vehicles is: (a) convex (b) concave (c) plane (d) cylindrical
2. Stars twinkle because of: (a) reflection (b) dispersion (c) atmospheric refraction (d) total internal reflection
3. A person who cannot see distant objects clearly needs: (a) a convex lens (b) a concave lens (c) a cylindrical lens (d) a bifocal lens
4. If the refractive index of a medium is √2, its critical angle is: (a) 30° (b) 45° (c) 60° (d) 90°
5. In a prism, the colour deviated most is: (a) red (b) yellow (c) green (d) violet
6. To an astronaut in space, the sky appears black because: (a) there is no atmosphere to scatter light (b) there is no light (c) the Sun is too far (d) space absorbs blue light
7. A convex lens has a focal length of 25 cm. Its power is: (a) +4 D (b) +0.25 D (c) −4 D (d) +25 D
8. A plane mirror is moved 1 m away from a stationary object. The image moves through: (a) 1 m (b) 2 m (c) 0.5 m (d) 0

Answers:

1. (a). Erect, diminished image with a wide field of view.
2. (c). Changing layers of air bend starlight by varying amounts.
3. (b). Myopia.
4. (b). sin C = 1/√2.
5. (d). Violet has the highest refractive index in glass.
6. (a). Scattering needs air.
7. (a). 1/0.25 m.
8. (b). The image moves twice as far as the mirror.

What to do next

• Draw the concave-mirror image table from memory, then do the same for a convex lens (it follows the same pattern with F and 2F).
• Make a list of every "why" in this guide (blue sky, red sunset, twinkling, mirage, diamond) with its one-word cause.
• Solve ten power and combination-of-lens questions, always converting to metres.
• Revise waves and sound, then continue to electricity.