Physics

medium importance~1 Q in Tier 127 formulas⚡ 12 shortcuts6 subtopics

Overview Learn (6)Formulas (27)Examples (4)Practice (121)

Light — mirrors, lenses, eye, dispersion and scattering

⏱ 6 min read🧩 6 question types🎯 22 practice Q

The idea in one minute

Light travels in straight lines at about 3 × 10⁸ m/s in vacuum. Mirrors reflect it, lenses and glass bend it, and a prism splits it into colours. Exams ask which mirror or lens to use, eye defects, and why the sky is blue.

Light, the basics

Light is a form of energy that makes things visible. In one medium it moves in straight lines. That is why shadows form.

The speed of light in vacuum is $c \approx 3 \times 10^8$ m/s. It is the highest speed in the universe.
Light slows down in water and glass.
Refractive index is $n = \dfrac{c}{v}$ . In glass, $n \approx 1.5$ , so light moves at about $2 \times 10^8$ m/s.
Sunlight takes about 8 minutes 20 seconds to reach the Earth.
Diamond has a very high refractive index, about 2.42. It has a small critical angle, so it sparkles.

Mirrors and their jobs

Mirror	Image	Standard uses
Plane	Virtual, erect, same size, laterally inverted	Looking glass, periscope
Concave (converging)	Real and inverted if the object is far. Magnified virtual image if close.	Shaving and make-up mirror, dentist's mirror, headlight and torch reflectors, solar furnace
Convex (diverging)	Always virtual, erect, diminished. Wide field of view.	Rear-view mirror, mirrors at road bends

A concave mirror brings parallel rays to a focus. So it collects the Sun's heat, or sends lamp light out as a beam.

Tip: Need a wide view? Choose convex. Need an enlarged image or a beam? Choose concave.

Lenses

A convex lens is thicker in the middle. It converges rays. It is used in a magnifier, camera, projector, microscope, telescope objective and the eye.

Object inside F: image is magnified, erect and virtual (a magnifier).
Object beyond 2F: image is real, inverted and diminished (a camera).

A concave lens always forms a virtual, erect, diminished image of a real object. It corrects short sight.

Power is $P = \dfrac{1}{f}$ , with f in metres. The unit is the dioptre (D). Convex power is positive. Concave power is negative. For thin lenses in contact, powers simply add.

Example: A lens of focal length 25 cm has $f = 0.25$ m. Its power is $\dfrac{1}{0.25} = +4$ D.

The eye and its defects

The eye lens forms a real, inverted image on the retina. The brain reads it upright.

Nearest clear vision is about 25 cm. The far point is at infinity.
Rods work in dim light. Cones sense colour.
Persistence of vision is about 1/16 s. It makes cinema possible.

Defect	What goes wrong	Correction
Myopia (short sight)	Image forms in front of the retina	Concave lens
Hypermetropia (long sight)	Image forms behind the retina	Convex lens
Presbyopia	Old age, lens loses flexibility	Bifocal lens
Astigmatism	Uneven curve of the cornea	Cylindrical lens
Cataract	Lens turns opaque	Surgery

Colour blindness is not a lens problem. The cones lack some colour sensors. No lens can correct it.

Refraction and total internal reflection

Light bends when it passes at a slant between clear media. This is refraction. The speed changes. Light bends towards the normal in a denser medium.

A pencil in water looks bent. A pool looks shallower.
Stars twinkle because of shifting layers of air. Planets hardly twinkle.
The Sun is seen about 2 minutes before actual sunrise and after actual sunset.

Total internal reflection (TIR) happens when light goes from a denser to a rarer medium beyond the critical angle. All the light reflects back. It gives the sparkle of a diamond, optical fibres, the endoscope and the mirage.

Dispersion and scattering

White light is a mixture of seven colours, VIBGYOR. A prism splits it. This is dispersion. Violet bends most and red bends least. Newton recombined the colours with a second prism.

A rainbow forms by refraction, dispersion and internal reflection in raindrops. It is seen with the Sun behind you. In the primary rainbow, red is on the outside.

Scattering by air molecules is stronger for short wavelengths. So:

The sky looks blue.
The Sun looks red at sunrise and sunset.
Danger signals are red, because red scatters least and is seen from far.
The sky looks black to astronauts, because space has no air to scatter light.

Note: The Raman effect was found by C.V. Raman on 28 February 1928. That day is National Science Day. He won the Nobel Prize in 1930.

Light primaries are red, green and blue. Red + green is yellow, green + blue is cyan, red + blue is magenta. All three make white. A red rose in green light looks almost black, because it reflects only red.

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common3 practice Q

Mirror, image and use

How to spot it:

The question asks which mirror is a rear-view, shaving or dentist's mirror, or which image a convex mirror forms, or plane mirror properties.

Method

Let the job decide. A wide upright view needs convex. An enlarged close view or a beam needs concave.
A convex mirror always gives a virtual, erect, diminished image.
A plane mirror image is virtual, erect, same size and laterally inverted.

Why it works:

Each mirror bends rays in a fixed way, so each has fixed jobs.

Try this

A dentist's mirror is a:

Show solution

The mirror is held close to the tooth.
The image must be erect and magnified.
Only a concave mirror does that.

Answer

Concave mirror

Type 2very common3 practice Q

Lens, image and use

How to spot it:

The question says 'Which lens is used in a magnifier / camera / projector?', 'a concave lens always forms ...' or 'which lens converges light'.

Method

A converging lens is a convex lens: magnifier, camera, projector, eye lens.
A diverging lens is a concave lens. For real objects the image is virtual, erect and diminished.
For a magnifier, keep the object inside the focal length.

Why it works:

Convex lenses converge light. Concave lenses spread it out.

Try this

A camera lens produces an image that is:

Show solution

The object is far beyond 2F.
The image lands between F and 2F.
It is real, inverted and diminished.

Answer

Real, inverted and diminished

Type 3very common3 practice Q

Eye defects and correction

How to spot it:

A defect (myopia, hypermetropia, presbyopia, astigmatism, cataract, colour blindness) is given with its cause or lens.

Method

Short-sighted is myopia, so choose a concave lens. Long-sighted is hypermetropia, so choose a convex lens.
Old-age trouble with near and far points to a bifocal lens. Uneven cornea points to a cylindrical lens. A cloudy lens is cataract, treated by surgery.
Colour blindness has no lens correction, so reject any lens option.

Why it works:

Each defect has one fixed cause and one fixed cure.

Try this

Presbyopia of old age is corrected by:

Show solution

Both near and far vision are weak.
One lens needs two parts.
Bifocal lenses have a convex lower part and a concave upper part.

Answer

Bifocal lenses

Type 4common3 practice Q

Lens power and light-speed numericals

How to spot it:

A focal length is given and power is asked (or the reverse), lenses are in contact, or a distance is divided by the speed of light.

P=\frac{1}{f(\text{m})}\ (\text{dioptre}),\quad P=P_1+P_2,\quad t=\frac{d}{c}

Method

Convert the focal length to metres first.
Use P = 1/f. Convex is positive and concave is negative.
For lenses in contact, add the powers.
For light travel time, use t = d ÷ (3 × 10⁸ m/s).

Why it works:

The dioptre means 1 per metre, so the metre conversion is the only trap.

Try this

Two thin lenses of powers +2 D and −0.5 D are placed in contact. Find the power and nature of the combination.

Show solution

Add the powers: 2 + (−0.5) = 1.5.
The net power is positive.

Answer

+1.5 D, a converging combination

Type 5very common4 practice Q

Refraction and total internal reflection effects

How to spot it:

A phenomenon (bent pencil, shallow pool, twinkling star, early sunrise, mirage, optical fibre, diamond sparkle) with its cause asked.

Method

If an object looks bent, shifted or shallow, or stars twinkle, or the Sun rises early, the cause is refraction.
If light stays inside (diamond, optical fibre, endoscope) or a mirage forms, the cause is total internal reflection.
TIR needs light going from a denser to a rarer medium beyond the critical angle.

Why it works:

Refraction comes from a change of speed between media.

Try this

Why do stars twinkle but planets hardly do?

Show solution

Starlight refracts through shifting layers of air.
So its brightness flickers.
Planets are closer and act as extended sources, so the changes average out.

Answer

Atmospheric refraction

Type 6very common4 practice Q

Dispersion, scattering and colour facts

How to spot it:

The question asks why the sky is blue, why danger signals are red, the VIBGYOR order, which colour bends most, rainbow facts, or an object's colour in coloured light.

Method

Blue sky, red sunset and red danger signals all come from scattering.
In a prism violet bends most and red bends least.
For a rainbow, remember dispersion plus internal reflection in raindrops, the Sun behind you, and red on the outer edge of the primary bow.
A body shows the colour it reflects. It looks black in light it fully absorbs.

Why it works:

Short wavelengths scatter most, and different colours bend by different amounts.

Try this

A red rose is seen in green light. What colour does it appear?

Show solution

The rose reflects only red light.
Green light has no red in it.
So the rose absorbs the green light.

Answer

Almost black

Formula sheet

Power of a lens

P = \frac{1}{f\,(\text{m})} = \frac{100}{f\,(\text{cm})}

unit dioptre

Lens formula

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

Cartesian sign convention

Mirror formula

\frac{1}{f} = \frac{1}{v} + \frac{1}{u}

f = R/2

Refractive index

n = \frac{c}{v}

c = 3 × 10⁸ m/s

Shortcuts that save time

⚡ Eye defect and its lens

Myopia goes with concave. Hypermetropia goes with convex. A short-sighted eye needs a diverging lens to push the image back onto the retina.

Example

A person who cannot see distant objects clearly needs which lens?

Show solution

Cannot see far means short sight, or myopia.
Myopia goes with a concave lens.

Answer

A concave (diverging) lens

⚡ Mirror by job

Need a wide view? Use convex (rear-view). Need an enlarged image or a focused beam? Use concave (shaving, dentist, headlight).

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Explaining the blue sky by reflection or refraction.

The cause is scattering of short wavelengths.

Mistake 02

Saying red bends most in a prism.

Violet bends most and red bends least.

Mistake 03

Choosing a concave mirror for a vehicle rear-view.

Vehicles use convex mirrors for a wide view.

Mistake 04

Leaving the focal length in centimetres in P = 1/f.

Convert to metres first: 25 cm = 0.25 m.

Mistake 05

Offering a lens as the cure for colour blindness.

No lens can correct it.

Quick revision

Read this the night before the exam.

c = 3 × 10⁸ m/s. n = c/v. Sunlight takes about 8 min 20 s to reach Earth.
Plane mirror: lateral inversion. Concave: shaving, dentist, headlight. Convex: rear-view.
P = 1/f (metres) in dioptre. Powers add for lenses in contact.
Myopia: concave. Hypermetropia: convex. Presbyopia: bifocal. Astigmatism: cylindrical. Cataract: surgery.
TIR: diamond sparkle, optical fibre, mirage. Refraction: bent pencil, twinkling, early sunrise.
Violet bends most in a prism. Blue sky, red sunset and red danger signals come from scattering.

Practice: 22 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 10 questions

Suggested time 3 min · wrong answers go to your mistake notebook automatically.

Continue learning