Revision: Optics JEE Main Optics

When travelling obliquely from one medium to another, the direction of propagation of light in the second medium changes. This phenomenon is known as refraction of light.

OR

Light changes its direction when going from one transparent medium to another transparent medium. This is called the refraction of light.

OR

The bending of the light ray from its path in passing from one medium to the other medium is called 'refraction' of light.

Refracted light is the part of light enters into the other medium and travels in a straight path but in a direction different from its initial direction and is called the refracted light.

The change in the direction of the path of light when it passes from one transparent medium to another transparent medium is called refraction. The refraction of light is essentially a surface phenomenon.

Light rays that are parallel to the principal axis of a concave mirror converge at a specific point on its principal axis after reflecting from the mirror. This point is known as the principal focus of the concave mirror.

When a ray of light propagates from a denser medium to a rarer medium, the angle of incidence for which the angle of refraction is 90° is called the critical angle.

When rays of light parallel to the principal axis of a mirror are incident on it, the rays after reflection either converge at a point or appear to diverge from a point. The distance of that point from the pole of the mirror is known as the focal length of the mirror.

Angular magnification or magnifying power of an optical instrument is defined as the ratio of the visual angle made by the image formed by that optical instrument (β) to the visual angle subtended by the object when kept at the least distance of distinct vision (α).

The resolving power of an astronomical telescope is defined as the reciprocal of the smallest angular separation between two point objects whose images can just be resolved by the telescope.

R.P = `(1.22 lambda)/D`

Resolving power is the ability of the telescope to distinguish clearly between two points whose angular separation is less than the smallest angle that the observer’s eye can resolve.

The apparent change in the frequency of sound heard by a listener, due to relative motion between the source of sound and the listener is called Doppler effect in sound.

When the source and the observer are in relative motion with respect to each other and to the medium in which sound propagates, the frequency of the sound wave observed is different from the frequency of the source. This phenomenon is called Doppler Effect.

The distance of the image from the pole of the mirror is called the image distance (v).

In a spherical mirror, the distance of the object from its pole is called the object distance (u).

The distance of the principal focus from the pole is called the focal length (f).

The phenomenon of the splitting of white light by a prism into its constituent colours is known as dispersion of light.

When a beam of white light or composite light is refracted through any transparent media such as glass or water, it is split into its component colours. This phenomenon is called ‘dispersion of light’.

On passing white light through a prism, the band of colours seen on a screen is called the spectrum.

or

The band of the coloured components of a light beam is called its spectrum.

The phenomenon of splitting of white light by a prism into its constituent colours is known as dispersion.

OR

The splitting of light into its component colours is called dispersion.

OR

The process of separation of light into its component colours while passing through a medium is called the dispersion of light.

Normal to the surface of a mirror at any point is the straight line at the right angle to the tangent drawn at that point.

Mirrors whose reflecting surfaces are spherical are called spherical mirrors.

OR

A spherical mirror is a part of a hollow sphere, whose one side is silvered and coated with red oxide and the other side is the reflecting surface.

The centre of the reflecting surface of a spherical mirror is a point called the pole. The pole is usually represented by the letter P.

OR

The central point of the reflecting surface of the mirror is called the 'pole' of the mirror.

A spherical mirror, whose reflecting surface is curved inwards, that is, faces towards the centre of the sphere, is called a concave mirror.

OR

A concave mirror is one whose reflecting surface is towards the centre of the sphere of which the mirror is a part.

A spherical mirror whose reflecting surface is curved outwards, is called a convex mirror.

OR

A convex mirror is one whose reflecting surface is away from the centre of the sphere of which the mirror is a part.

The reflecting surface of a spherical mirror forms a part of a sphere. This sphere has a centre. This point is called the centre of curvature of the spherical mirror. It is represented by the letter C.

OR

The centre of the sphere of which the mirror forms a part, is called the ‘centre of curvature' of the mirror.

The radius of the sphere of which the reflecting surface of a spherical mirror forms a part is called the radius of curvature of the mirror. It is represented by the letter R.

OR

The radius of the sphere of which the mirror forms a part, is called the 'radius of curvature' of the mirror.

The distance between the pole and the principal focus is called the focal length (f) of a spherical mirror.

Pole is the centre of the reflecting surface, in this case, a spherical mirror.

Aperture is the distance between the extreme points on the periphery of the mirror.

 Centre of curvature is the centre of the imaginary sphere to which the mirror belongs.

Principal focus of a spherical mirror is a point on the principal axis of the mirror, where all the rays travelling parallel to the principal axis and close to it after reflection from the mirror, converge to or appear to diverge from.

“A mirror which is made from a part of a hollow sphere is called Spherical Mirror.

“A mirror made by silvering the inner surface such that reflection takes place from the bulging surface” is called Convex Mirror.
The Centre of curvature is towards the silvered surface.

“A mirror made by silvering the outer or the bulging surface such that the reflection takes place from the concave surface.” Centre of curvature is towards the reflecting surface.

Pole “is the mid-point of the mirror”.

The centre of a hollow sphere of which the mirror forms a part is called the centre of curvature.

An imaginary line passing through the pole and the centre of curvature of a spherical mirror is called principal axis.

It is a point on the principal axis, where a beam of light, parallel to the principal axis, after reflection actually meet.

The linear distance between the pole and the center of curvature is called the radius of curvature.

The linear distance between the pole and the principal focus is called focal length.

The focus of a concave mirror is a point on the principal axis of the mirror, where all the rays travelling parallel to the principal axis and close to it after reflection from the mirror converge to that point.

A straight line passing through the pole and the centre of curvature of a spherical mirror. This line is called the principal axis.

OR

The straight line joining the pole and the centre of curvature of the mirror and extended on both sides is called the 'principal axis' of the mirror.

The principal axis is the straight line passing through the pole and the centre of curvature.

The bouncing of light by any smooth or polished surface is called.

The phenomenon due to which a parallel beam of light traveling through a certain medium, on striking some polished surface, bounces off from it, as a parallel beam, in some other direction, is called regular reflection.

The deviation of the incident light rays produced by a lens on refraction through it, is a measure of its power.

or

The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter P.

OR

The power (P) of a thin lens is equal to the reciprocal of its focal length (f) measured in metres.

Power of a lens is defined as the ability of a lens to bend the rays of light. It is given by the reciprocal of focal length in metre.

The power of a lens is a measure of the deviation produced by it in the path of rays refracted through it.

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

Magnification (m) = \[\frac{\text{Height of the image (}h'\text{)}}{\text{Height of the object (}h\text{)}}\] = \[\frac {h'}{h}\]

Magnification in terms of object and image distances:

Magnification (m) = \[\frac {h'}{h}\] = -\[\frac {v}{u}\]

Magnification (m) = \[\frac{\text{Height of the Image}}{\text{Height of the object}}=\frac{h^{\prime}}{h}\]

Magnification in terms of object and image distances:

Magnification (m ) = \[\frac {h'}{h}\] = \[\frac {v}{u}\]

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

Power of lens (in D) = \[\frac{1}{\text{focal length (in metre)}}\]

or

P = \[\frac {1}{f}\]

or

P = \[\frac {1}{f (m)}\]

Power of a Lens in a Medium:

P = (n₂ - n₁)\[\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)\] = \[\frac {n_1}{f}\]

According to the laws of reflection:

• At the point of incidence, the incident rays, reflected rays, and normal to the reflecting surface all lie in the same plane.
• On opposing sides of the normal are the incident and reflected rays.
• The angle of incidence and the angle of reflection are the same. i.e., ∠i = ∠r.

Explanation:

                Reflection of light

XY: Plane reflecting surface

AB: Plane wavefront

RB₁: Reflecting wavefront

A₁M, B₁N: Normal to the plane

∠AA₁M = ∠BB₁N = ∠i = Angle of incidence

∠TA₁M = ∠QB₁N = ∠r = Angle of reflection

A plane wavefront AB is advancing obliquely towards the plane reflecting surface XY. The AA₁ and BB₁ are incident rays.

When ‘A’ reaches XY at A₁, then the ray at ‘B’ reaches point ‘P’, and it has to cover the distance PB₁ to reach the reflecting surface XY.

Let ‘t’ be the time required to cover the distance PB₁. During this time interval, secondary wavelets are emitted from A₁ and will spread over a hemisphere of radius A₁R, in the same medium. The distance covered by secondary wavelets to reach from A₁ to R in time t is the same as the distance covered by primary waves to reach from P to B₁. Thus, A₁R = PB₁ = ct.

All other rays between AA₁ and BB₁ will reach XY after A₁ and before B₁. Hence, they will also emit secondary wavelets of decreasing radii.

The surface touching all such hemispheres is RB₁ which is the reflected wavefront, bounded by reflected rays A₁R and B₁Q.

Draw A₁M ⊥ XY and B₁N ⊥ XY.

Thus, the angle of incidence is ∠AA₁M = ∠BB₁N = i, and the angle of reflection is ∠MA₁R = ∠NB₁Q = r.

∠RA₁B₁ = 90 − r

∠PB₁A₁ = 90 − i

In ΔA₁RB₁ and ΔA₁PB₁

∠A₁RB₁ = ∠A₁PB₁

A₁R = PB₁    ....(Reflected waves travel an equal distance in the same medium in equal time.)

A₁B₁ = A₁B₁     ....(Common side)

∴ ΔA₁RB₁ ≅ ΔA₁PB₁

∴ ∠RA₁B₁ = ∠PB₁A₁

∴ 90 − r = 90 − i

∴ i = r

Also from the figure, it is clear that incident rays, reflected rays, and normal lie in the same plane.

This explains the laws of reflection of light from a plane reflecting surface on the basis of Huygen’s wave theory.

Frequency, wavelength, and speed of light do not change after reflection. If reflection takes place from a denser medium, then the phase changes by π radians.

AB = Incident wavefront

CD = Reflected wavefront

XY = Reflecting surface

If c be the speed of light and t be the time taken by light to go from B to C or A to D or E to G through F, then

t = `(EF)/C + (FG)/C`

= `(AF sin i)/C + (FC sin r)/C`

= `(AC sin r + AF(sin i - sin r))/C`

For rays of light from different parts of the incident wavefront, the values of AF are different. But light from different points of the incident wavefront should take the same time to reach the corresponding points on the reflected wavefront.

So, ‘t’ should not depend upon AF.

This is possible only if sin i – sin r = 0.

i.e., sin i = sin r

⇒ i = r

Hence proved.

• Dispersion is the splitting of white light into seven colours (VIBGYOR) when it passes through a prism or similar transparent medium.
• Human eyes can detect light with wavelengths ranging from 400 nm (violet) to 700 nm (red).
• Different colours travel at different speeds in a medium like glass, so each colour has a different refractive index.
• Violet light bends the most, and red light bends the least, as it passes through a prism, producing a spectrum.
• A rainbow is formed due to dispersion, refraction, and internal reflection of sunlight by raindrops acting as tiny prisms.

• Reflection occurs when light bounces off a smooth surface like a mirror, following fixed laws.
• Plane mirrors always form virtual, erect, and same-sized images that are laterally inverted.
• Curved surfaces (like a spoon) act as spherical mirrors, changing the image size and orientation depending on the object's position.