Master the basics - and everything after gets easier

What it is

Light bends (refracts) when its speed changes on moving between media of different densities.

Answer

Light bends because its speed changes when it moves from one medium to another. Glass is optically denser than air, so light slows down on entering glass and bends towards the normal. This bending of light due to a change in speed is called refraction.

What it is

The mirror formula links focal length, object distance and image distance for a curved mirror.

Answer

The mirror formula relates focal length f, image distance v and object distance u as 1/f = 1/v + 1/u. By the New Cartesian sign convention, distances are measured from the pole; distances measured against the incident light (to the left) are negative, so for a concave mirror f and u are negative, and a real image distance v is also negative.

What it is

For a conductor at steady temperature, voltage = current x resistance (V = IR).

Answer

Ohm's law states that, at constant temperature, the current I through a conductor is directly proportional to the potential difference V across it, so V = IR. Resistance R is the property of a conductor that opposes the flow of current; it is the ratio of potential difference to current, R = V/I, measured in ohm.

What it is

Electric power is the rate of using electrical energy: P = VI (also I^2 R or V^2 / R).

Answer

Using Ohm's law, V = IR = 2 x 5 = 10 V. Power dissipated P = VI = 10 x 2 = 20 W (equivalently P = I^2 R = 4 x 5 = 20 W).

What it is

A current in a straight wire creates circular magnetic field lines around it.

Answer

If you hold the straight conductor in your right hand with the thumb pointing in the direction of the current, the curled fingers show the direction of the concentric circular magnetic field lines around the wire.

What it is

The power of a lens tells how strongly it bends light; it is the reciprocal of its focal length in metres.

Answer

Power P = 1 / f, where f is the focal length in metres. Here f = 25 cm = 0.25 m, so P = 1 / 0.25 = +4 dioptres (D). The power is positive because it is a convex (converging) lens.

What it is

The sky is blue because tiny air molecules scatter blue light much more than red.

Answer

Sunlight is scattered by the tiny molecules of air in the atmosphere. Blue light has a shorter wavelength and is scattered much more strongly than red light. As this scattered blue light reaches our eyes from all directions, the clear sky appears blue. At sunset the light travels a longer path, most of the blue is scattered away, and the remaining red light makes the sky look reddish.

What it is

In series, resistances add up; in parallel, the combined resistance is smaller than the smallest one.

Answer

In a series combination the resistors are joined end to end so the same current flows through each, and the total resistance is the sum: R = R1 + R2 + R3. In a parallel combination the resistors are connected between the same two points and share the current, so the reciprocals add: 1/R = 1/R1 + 1/R2 + 1/R3. As a result the total resistance in parallel is always less than the smallest individual resistance. Household circuits are wired in parallel so every appliance gets the full voltage.

What it is

Air molecules scatter shorter (blue) wavelengths much more than red, so the clear sky looks blue.

Answer

As sunlight passes through the atmosphere it is scattered by the tiny molecules of air. Scattering is much stronger for shorter wavelengths, so blue light is scattered far more than red light. This scattered blue light reaches our eyes from every part of the sky, making a clear sky look blue. Near sunrise and sunset the light travels a much longer path through the air, most of the blue is scattered away, and the Sun appears red.

What it is

A changing magnetic field around a conductor induces a current in it - the reverse of the motor effect.

Answer

Electromagnetic induction is the production of an electric current in a conductor whenever the magnetic field around it changes, for example by moving a magnet into or out of a coil. The changing field sets up a potential difference that drives a current. Discovered by Faraday, it is the principle behind the electric generator. The induced current can be increased by moving the magnet faster, using a stronger magnet, or increasing the number of turns in the coil.

What it is

The power of a lens measures how strongly it converges or diverges light.

Answer

Power = 1 / focal length (in metres) = 1 / 0.5 = +2 dioptre (D). A convex (converging) lens has positive power; the shorter its focal length, the higher its power.

What it is

The refractive index of a medium is how many times slower light travels in it than in vacuum.

Answer

Refractive index n = speed in vacuum / speed in medium = (3 x 10^8) / (2 x 10^8) = 1.5. A larger refractive index means light travels more slowly in the medium and bends more on entering it.

What it is

Resistors joined end to end (in series) have a combined resistance equal to their sum.

Answer

In series, resistances add: R = R1 + R2 = 10 + 20 = 30 ohm. The total resistance in a series combination is always greater than the largest individual resistor.

What it is

Electric current is the rate of flow of electric charge through a conductor.

Answer

Current = charge / time = 30 / 60 = 0.5 ampere (A). Current tells us how much charge flows each second, so more charge in less time means a larger current.

What it is

The heat power produced in a resistor depends on the square of the current and the resistance.

Answer

Power = I^2 x R = 2^2 x 5 = 4 x 5 = 20 watt (W). Because the current is squared, doubling the current to 4 A would give 4^2 x 5 = 80 W - four times the heat.

What it is

Resistors connected across the same two points (in parallel) give a combined resistance smaller than any one of them.

Answer

For two resistors in parallel, R = (R1 x R2) / (R1 + R2) = (10 x 20) / (10 + 20) = 200 / 30 = 6.67 ohm. Notice the total is smaller than either resistor, because the current now has more than one path to flow through.

What it is

The charge that flows is the current multiplied by the time it flows for.

Answer

Charge = current x time = 2 x 30 = 60 coulomb (C). A larger current, or a longer time, delivers more charge past a point in the circuit.

What it is

The electrical energy used is the power of a device multiplied by the time it runs, often measured in kilowatt-hours (units).

Answer

Energy = power x time = 1000 W x 5 h = 5000 Wh = 5 kilowatt-hours (kWh), that is 5 units. One unit of electricity is one kilowatt-hour - a 1000 W appliance running for one hour.

What it is

The potential difference (voltage) between two points is the work done to move each unit of charge between them.

Answer

Potential difference = work done / charge = 60 / 5 = 12 volt (V). Voltage measures the energy given to each coulomb of charge, so 1 V means 1 J of work per coulomb.

What it is

From Ohm's law, the resistance of a conductor is the voltage across it divided by the current through it.

Answer

Resistance = voltage / current = 12 / 2 = 6 ohm. This is Ohm's law V = IR rearranged as R = V / I; for a fixed voltage, a larger current means a smaller resistance.

What it is

The heat produced in a resistor is the square of the current times the resistance times the time.

Answer

Heat H = I^2 x R x t = 2^2 x 5 x 10 = 4 x 5 x 10 = 200 joule (J). Because the current is squared, doubling it would produce four times as much heat.

What it is

Electric power is the product of the voltage across a device and the current through it.

Answer

Power = voltage x current = 12 x 2 = 24 watt (W). This is the rate at which the device converts electrical energy; combined with Ohm's law it also gives P = I^2 R and P = V^2 / R.

What it is

The focal length of a spherical mirror is half its radius of curvature.

Answer

Focal length = radius of curvature / 2 = 40 / 2 = 20 cm. The principal focus of a spherical mirror lies exactly midway between the pole and the centre of curvature.

What it is

The speed of light in a medium is the speed in vacuum divided by the medium's refractive index.

Answer

Speed in medium = c / n = (3 x 10^8) / 1.5 = 2 x 10^8 m/s. The larger the refractive index, the more the light slows down, and the more it bends on entering the medium.

What it is

The cost of electricity is the number of units (kilowatt-hours) used multiplied by the rate per unit.

Answer

Cost = units x rate = 100 x 6 = 600 rupees. One unit is one kilowatt-hour, so using fewer units - by switching off idle appliances - directly reduces the bill.

What it is

The current a device draws is its power divided by the supply voltage.

Answer

Current = power / voltage = 1100 / 220 = 5 A. This comes from P = V x I rearranged as I = P / V, and it decides the fuse rating the appliance needs.

What it is

The power dissipated in a resistor is the square of the voltage divided by the resistance.

Answer

Power = V^2 / R = 220^2 / 484 = 48400 / 484 = 100 W. This form comes from combining P = VI with Ohm's law V = IR, and shows that a smaller resistance draws more power at a fixed voltage.

What it is

In a series circuit the components share one path, while in a parallel circuit each has its own path.

Answer

In a series circuit there is only one path for the current, so if one bulb breaks the circuit is open and both bulbs go out. In a parallel circuit each bulb sits on its own branch and gets the full voltage, so if one breaks the other keeps glowing. That is why household wiring is done in parallel and each appliance also gets the same voltage.

What it is

A plane mirror forms a virtual, erect image of the same size, as far behind the mirror as the object is in front, and laterally inverted.

Answer

The image formed by a plane mirror is virtual (cannot be caught on a screen) and erect (upright). It is of the same size as the object. It is formed as far behind the mirror as the object is in front of it. The image is laterally inverted, meaning the left and right sides appear interchanged, which is why the word AMBULANCE is written in a mirror-reversed form on vehicles.

What it is

Concave mirrors converge light and can form real or virtual images; convex mirrors diverge light and always form small, virtual, erect images.

Answer

A concave mirror is used as a shaving or make-up mirror because, when the face is held close (within the focus), it forms a magnified, erect, virtual image; it is also used in torches and headlights to produce a parallel beam. A convex mirror is used as a rear-view mirror in vehicles because it always forms a small, erect, virtual image and gives a wide field of view, letting the driver see more traffic behind.

What it is

The mirror formula 1/v + 1/u = 1/f relates image distance, object distance and focal length.

Answer

For a concave mirror, f = -20 cm and the object distance u = -30 cm (New Cartesian convention). Using 1/v + 1/u = 1/f: 1/v = 1/f - 1/u = 1/(-20) - 1/(-30) = -1/20 + 1/30. Taking LCM 60: = -3/60 + 2/60 = -1/60. So v = -60 cm. The image is real, inverted and formed 60 cm in front of the mirror.

What it is

Refraction is the bending of light when it changes speed passing between media; the refractive index measures how much the speed changes.

Answer

The refractive index of a medium is the ratio of the speed of light in vacuum (or air) to the speed of light in that medium, that is n = c/v. A refractive index of 1.5 for glass means that light travels 1.5 times faster in vacuum than in glass, or equivalently that the speed of light in glass is 1/1.5 of its speed in vacuum. A higher refractive index means the medium is optically denser and bends light more.

What it is

A convex lens converges light and can form real or virtual images; a concave lens diverges light and always forms a small, virtual, erect image.

Answer

A convex (converging) lens is thicker in the middle and bends parallel rays of light to meet at a focus; it can form real, inverted images or a magnified virtual image, and is used in magnifying glasses, cameras and to correct hypermetropia. A concave (diverging) lens is thinner in the middle and spreads parallel rays apart; it always forms a small, erect, virtual image and is used to correct myopia (short-sightedness).

What it is

The lens formula 1/v - 1/u = 1/f relates image distance, object distance and focal length of a lens.

Answer

For a convex lens, f = +10 cm and the object distance u = -15 cm. Using 1/v - 1/u = 1/f: 1/v = 1/f + 1/u = 1/10 + 1/(-15) = 1/10 - 1/15. Taking LCM 30: = 3/30 - 2/30 = 1/30. So v = +30 cm. The image is real, inverted and formed 30 cm on the other side of the lens.

What it is

The power of a lens is the reciprocal of its focal length in metres, measured in dioptres.

Answer

The power of a lens P = 1/f, where f is the focal length in metres. Here f = 25 cm = 0.25 m, and the lens is convex so f is positive. P = 1/0.25 = +4 D. So the power of the lens is +4 dioptres. A concave lens would have a negative power.

What it is

The eye focuses light using the cornea and lens to form a real, inverted image on the retina.

Answer

The main parts of the human eye are: the cornea, the transparent front part where most refraction occurs; the iris, which controls the size of the pupil; the pupil, the opening that lets light in; the eye lens, which fine-tunes the focus; the retina, the light-sensitive screen where a real, inverted image forms; and the optic nerve, which carries signals to the brain. The ciliary muscles change the shape of the lens.

What it is

Accommodation is the ability of the eye lens to change its focal length to focus objects at different distances.

Answer

The power of accommodation is the ability of the eye lens to adjust its focal length so that objects at different distances can be focused sharply on the retina. When we look at a distant object, the ciliary muscles relax, the lens becomes thin and its focal length increases. When we look at a nearby object, the ciliary muscles contract, the lens becomes thick and its focal length decreases. However, the lens cannot become thinner or thicker beyond a limit, so there is a nearest point (about 25 cm) called the near point.

What it is

In myopia a person can see near objects clearly but not distant ones; it is corrected with a concave lens.

Answer

Myopia, or short-sightedness, is a defect of vision in which a person can see nearby objects clearly but cannot see distant objects distinctly. It is caused when the image of a distant object is formed in front of the retina, either because the eyeball is too long or the lens is too curved (its focal length is too short). It is corrected by using spectacles with a concave (diverging) lens of suitable power, which spreads the rays slightly so the image forms on the retina.

What it is

In hypermetropia distant objects are seen clearly but near ones are not; it is corrected with a convex lens.

Answer

Hypermetropia, or long-sightedness, is a defect in which a person can see distant objects clearly but cannot focus on nearby objects; the image of a near object forms behind the retina, because the eyeball is too short or the lens focal length is too long. It is corrected using a convex (converging) lens of suitable power. Presbyopia is a defect that comes with old age, in which the eye loses its power of accommodation because the ciliary muscles weaken and the lens becomes less flexible; it is often corrected with bifocal lenses.

What it is

A prism splits white light into its seven component colours because each colour bends by a different amount.

Answer

Dispersion of light is the splitting of white light into its seven constituent colours - violet, indigo, blue, green, yellow, orange and red (VIBGYOR) - when it passes through a prism. It occurs because light of different colours has different wavelengths and therefore bends (refracts) by different amounts in the prism; violet light bends the most and red light the least. The band of colours obtained is called a spectrum. A rainbow forms by dispersion of sunlight through raindrops.

What it is

Scattering of light by small particles explains the blue colour of the sky and the red colour of the Sun at sunrise and sunset.

Answer

The molecules of air and fine particles in the atmosphere scatter shorter wavelengths (blue) of sunlight much more strongly than longer wavelengths (red). During the day, this scattered blue light reaches our eyes from all directions, so the sky appears blue. At sunrise and sunset, sunlight travels a longer path through the atmosphere, so most of the blue light is scattered away and only the longer-wavelength red light reaches us, making the Sun appear reddish.

What it is

Electric current is the rate of flow of charge; potential difference is the work done to move a unit charge between two points.

Answer

Electric current is the rate of flow of electric charge through a conductor, given by I = Q/t, where Q is the charge and t is the time; its SI unit is the ampere (A). Potential difference between two points is the work done to move a unit positive charge from one point to the other, given by V = W/Q; its SI unit is the volt (V). A current flows only when there is a potential difference across the conductor.

What it is

Ohm's law states that current through a conductor is directly proportional to the potential difference across it at constant temperature.

Answer

Ohm's law states that, at constant temperature, the current I flowing through a conductor is directly proportional to the potential difference V across its ends, so V = IR, where R is the resistance. Rearranging, R = V/I = 12/3 = 4 ohm. So the resistance of the resistor is 4 ohm.

What it is

The resistance of a wire depends on its length, area of cross-section, material and temperature.

Answer

The resistance R of a conductor depends on four factors: it is directly proportional to its length L (a longer wire has more resistance); it is inversely proportional to its area of cross-section A (a thicker wire has less resistance); it depends on the nature of its material through a property called resistivity (rho); and it generally increases with temperature. These are combined in the relation R = rho L / A.

What it is

In a series combination, the same current flows through all resistors and the total resistance is the sum of the individual resistances.

Answer

In a series combination, the total (equivalent) resistance is the sum of the individual resistances: Rs = R1 + R2 + R3 = 2 + 3 + 5 = 10 ohm. So the total resistance is 10 ohm. In series, the same current flows through each resistor, and the total voltage is shared among them.

What it is

In a parallel combination, the voltage is the same across each resistor and the reciprocal of the total resistance is the sum of the reciprocals.

Answer

In a parallel combination, 1/Rp = 1/R1 + 1/R2 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. So Rp = 2 ohm. The equivalent resistance (2 ohm) is smaller than the smallest individual resistance (3 ohm), which is always true for parallel combinations. In parallel, the voltage across each resistor is the same.

What it is

When current flows through a resistor, heat is produced according to Joule's law of heating, H = I^2 R t.

Answer

Joule's law of heating states that the heat produced in a resistor is directly proportional to the square of the current (I^2), to the resistance (R) and to the time (t) for which the current flows: H = I^2 R t. Here H = 2^2 x 10 x 30 = 4 x 10 x 30 = 1200 J. So 1200 joules of heat is produced.

What it is

Electric power is the rate of consuming electrical energy, P = VI = I^2 R = V^2/R; energy is charged in kilowatt-hours.

Answer

The current drawn is found from P = VI, so I = P/V = 60/240 = 0.25 A. The resistance is found from P = V^2/R, so R = V^2/P = 240^2/60 = 57600/60 = 960 ohm. So the bulb draws 0.25 A and has a resistance of 960 ohm.

What it is

A magnetic field is the region around a magnet where its force can be felt; field lines show its direction and strength.

Answer

A magnetic field is the region around a magnet or a current-carrying conductor within which its magnetic force can be experienced. Magnetic field lines are used to represent it. Two properties are: the field lines emerge from the north pole and merge into the south pole outside the magnet (forming closed loops), and two field lines never intersect each other, because at a point the field can have only one direction. The field is stronger where the lines are closer together.

What it is

A current-carrying conductor produces a magnetic field around it, whose direction is given by the right-hand thumb rule.

Answer

When an electric current flows through a straight conductor, it produces a magnetic field in the form of concentric circles around the conductor. The direction of this field is given by the right-hand thumb rule (Maxwell's corkscrew rule): if you hold the conductor in your right hand with the thumb pointing in the direction of the current, then the curled fingers show the direction of the magnetic field lines around it.

What it is

A current-carrying conductor placed in a magnetic field experiences a force; its direction is given by Fleming's left-hand rule.

Answer

Fleming's left-hand rule states that if the thumb, forefinger and middle finger of the left hand are stretched mutually perpendicular, with the forefinger pointing in the direction of the magnetic field and the middle finger in the direction of the current, then the thumb points in the direction of the force (motion) experienced by the conductor. This rule gives the direction of force on a current-carrying conductor in a magnetic field, and it is the working principle of an electric motor.

What it is

A changing magnetic field around a coil induces an electric current in it; this is electromagnetic induction.

Answer

Electromagnetic induction is the phenomenon in which a changing magnetic field (for example, by moving a magnet near a coil or changing the current in a nearby coil) induces an electric current in a conductor or coil. Fleming's right-hand rule gives the direction of the induced current: if the thumb, forefinger and middle finger of the right hand are held mutually perpendicular, with the forefinger pointing in the direction of the magnetic field and the thumb in the direction of motion of the conductor, then the middle finger points in the direction of the induced current. It is the principle of the electric generator.

What it is

Household circuits use live, neutral and earth wires, with a fuse and earthing for safety.

Answer

In a domestic circuit, a fuse is a safety device made of a thin wire of low melting point connected in the live wire. If the current becomes too large due to a short circuit or overloading, the fuse wire heats up and melts, breaking the circuit and preventing fire and damage. The earth wire is connected to the metal body of appliances and to the ground; if the live wire touches the metal body, the earth wire provides a low-resistance path for the current to flow safely to the earth, protecting the user from a dangerous electric shock.