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.

OR

When a ray of light impinges on a polished, smooth, shiny surface, the rebounding of light within the same medium is called reflection of light.

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.

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.

or

When light passes from one transparent medium to another, its speed and direction change. This is called refraction.

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.

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.

The angle of incidence in the denser medium corresponding to an angle of refraction of 90° in the rarer medium is called the critical angle.

The phenomenon where light rays are completely reflected back into a medium instead of being refracted into another medium is called total internal reflection.

or

Complete reflection of a ray of light at the interface of an optically denser medium and a rarer medium, back into the denser medium.

The aberration caused by the spherical shape of the lens, where light rays at the edges focus at a different point than those near the centre, leading to a blurred image, is called spherical aberration.

The aberration that occurs due to the lens refracting different wavelengths of light at different angles, resulting in an image consisting of different colours without a single focussed image, is called chromatic aberration.

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.

An arc of seven colours with red on the inner edge and violet on the outer edge, caused by double total internal reflection inside water droplets, is called a secondary rainbow.

The optical illusion of water or distant objects caused by refraction of light due to temperature differences in air layers is called a mirage.

An arc of seven colours formed in the sky with red on the outer edge and violet on the inner edge, caused by single total internal reflection inside water droplets, is called a primary rainbow.

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).

An optical instrument that uses a single convex lens to magnify small objects is called a simple microscope.

An optical instrument that uses objective and eye piece lenses to magnify tiny objects in detail is called a compound microscope.

An optical instrument that uses objective and eye piece lenses to magnify distant terrestrial or celestial objects is called a telescope.

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

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 type of diffraction that occurs when the source or screen is at a finite distance from the diffracting object and fringes are not sharp and well-defined is called Fresnel diffraction.

The bending of light near the edge of an obstacle or slit and spreading into the region of geometrical shadow is called diffraction of light.

The type of diffraction that occurs when the source and the observation screen are far away (effectively at infinite distance) from the diffracting object and fringes are not sharp and well-defined is called Fraunhofer diffraction.

Alignment of dipole moments (permanent or induced) in the direction of an applied electric field is called polarisation.

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

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

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

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 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’.

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.

OR

The phenomenon in which white light splits into its constituent colours when it passes through a prism or another medium is called dispersion of light.

The angular separation between the two extreme rays of a dispersed beam of light is called angular dispersion.

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 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.

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.

OR

A spherical mirror is a piece cut out of a spherical surface, which can be concave or convex.

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.

OR

The reflecting surface is on the inner side of the sphere (converging mirror).

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.

OR

The reflecting surface is on the outer side of the sphere (diverging 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 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.

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 phenomenon of bouncing back of light rays in the same medium on striking a surface is called reflection of light.

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 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 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.

The ability of an optical instrument to produce distinctly separate images of two objects very close to each other is called the resolving power of the instrument.

The reciprocal of the limit of resolution is called its resolving power.

The quantity μ sin ⁡θ, where μμ is the refractive index of the medium between the object and the objective, is called the numerical aperture (N.A.) of the objective of the microscope.

The reciprocal of the least angular separation between the objects that are just resolved is called the resolving power of the telescope.

The minimum distance of separation between two objects when they can be observed as separate by an optical instrument is called the limit of resolution of that instrument.

n = \[\frac {\text {sin i}}{\text {sin r}}\] = \[\frac {c}{v}\] = \[\frac {\text {Real depth}}{\text {Apparent depth}}\]

d = t - \[\frac {t}{μ}\] = t\[\left(1-\frac{1}{\mu}\right)\]

1. M_Max = 1 + \[\frac {D}{f}\]
2. M_Min = \[\frac {D}{f}\]

M = m_o × M_e

1. \[\mathrm{M_{D.D.V}=\frac{f_{o}}{f_{e}}\left(1+\frac{f_{e}}{D}\right)}\]
2. M = \[\frac{\mathrm{f}_{0}}{\mathrm{f}_{0}}\]

\[\begin{array} {c}x_n=\frac{n\lambda D}{d}=n\beta \end{array}\]

\[\beta=\frac{\lambda D}{d}\]

\[\begin{array} {cc} & x_m=\frac{(2m-1)\lambda D}{2d} \end{array}\]

\[\alpha=\frac{\beta}{D}=\frac{\lambda}{d}\]

\[x_n-x_m=\left[n-\frac{(2m-1)}{2}\right]\beta\]

Defined as dipole moment per unit volume:

\[P=\frac{\text{dipole moment}}{\mathrm{volume}}=np\]

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

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

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

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

n = \[\frac {360°}{θ}\]

• If n is even → N = n − 1
• If n is odd → N = n (object not on bisector); N = n − 1 (object on bisector)
• If n is a fraction → N = integral part of n

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

R.P. = \[\frac {1}{d}\] = \[\frac{2\mu\sin\theta}{\lambda}\]

where μ sin⁡ θ is the Numerical Aperture (N.A.) of the objective.

R.P. = \[\frac{1}{d\theta}=\frac{D}{1.22\lambda}\]

R.P. = \[\frac {1}{\text {Limit of resolution}}\]

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.

Statement:

When unpolarised light is incident at polarising angle i_B on an interface separating air from a medium of refractive index μ, then the reflected light is plane polarised (perpendicular to the plane of incidence), provided:

Additional condition at polarising angle:

i.e., the reflected plane polarised light is at right angles to the refracted light.

OR

Statement:

• When the angle of incidence equals the polarising angle (θ_B), the reflected and refracted rays are perpendicular to each other.
• "The refractive index of a medium is equal to the tangent of the polarising angle θ_B."

• The angle of incidence ∠i = angle of reflection ∠r.
• The incident ray, reflected ray, and normal lie in one plane; both rays are on either side of the normal.

Convex lens: Thicker at the middle, thinner at the edges, converges parallel rays.

• Types: Double-convex, Plano-convex, Concavo-convex.

Concave lens: Thinner at the middle, thicker at the edges, diverges parallel rays.

• Types: Double-concave, Plano-concave, Convexo-concave.

Important Terms:

• Principal Axis: Straight line through the centres of curvature of two surfaces.
• Optical Centre (O): Ray passing through it goes undeviated with no lateral displacement.
• Principal Focus (F): Point where parallel rays converge (convex) or appear to diverge (concave) after refraction.
• Aperture: Effective diameter of light-transmitting area; Intensity ∝ (Aperture)²

Lens Maker's Formula:

\[\frac{1}{f}=(\mu-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\]

Where:

• f = focal length, μ = refractive index of lens material
• R₁, R₂ = radii of curvature of the two surfaces

New Cartesian Sign Conventions for Lens:

• Distances measured from optical centre.
• Along incident light → positive; against incident light → negative.
• For convex lens: f is positive; for concave lens: f is negative.

Rules for Image Formation:

1. Ray through optical centre → passes undeviated.
2. Ray parallel to principal axis → passes through F₂ (convex) or appears to come from F₁ (concave).
3. Ray towards/through first focus F₁ → emerges parallel to principal axis.

Lens Formula:

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

• A prism is a transparent medium bounded by two polished plane surfaces inclined at an angle (< 90°).
• The angle between the refracting faces = Refracting angle (A).
• A ray of light undergoes two refractions passing through a prism.

Angle of Deviation:

Minimum Deviation (δ_min):

• Occurs when i₁ = i₂ = i → ray passes symmetrically.
• At minimum deviation: \[r_1=r_2=r=\frac{A}{2}\]
• Minimum deviation: \[\delta_{min}=2i-A\]
• Angle of incidence at minimum deviation: \[i=\frac{A+\delta_{min}}{2}\]

Refractive Index of Prism:

• An optical instrument uses the principles of optics to enhance, modify, or analyse light for specific purposes.
• They manipulate light through reflection, refraction, diffraction, or interference.
• Common instruments: simple microscope, compound microscope, telescope.

Astronomical (Refracting) Telescope:

• Used to view distant objects.
• Objective lens (large focal length) forms image A'B' at its focus → acts as object for eyepiece.
• Eyepiece forms the final virtual, magnified image A''B''.

Magnifying Power: \[MP=\frac{\text{Visual angle with instrument}(\beta)}{\text{Visual angle for unaided eye}(\alpha)}\]

Resolving Power of Telescope:

• Ability to produce distinct images of two closely spaced objects.
• Angular separation between two resolvable objects: \[\sin\theta=1.22\frac{\lambda}{d}\]​ (Rayleigh's criterion), where d = aperture.
• Resolving power is inverse of angular separation.
• Larger aperture → better resolving power.

Types of Telescope:

• Refracting telescope: Uses two convex lenses; large objective + small eyepiece.
• Reflecting telescope: Uses concave mirror to reflect light internally; secondary mirror directs to eyepiece.
• Keplerian telescope: Converging lens as eyepiece → inverted image.
• Galilean telescope: Diverging lens as eyepiece → erect image.
• Magnification of Refracting Telescope: \[M=\frac{f_{o}}{f_{e}}\]

• Every point on a wavefront acts as a secondary source (point source) that emits new spherical wavelets in all directions with the same speed as the original wave.
• The new (forward) wavefront at any later time is the common tangential envelope (tangent surface) to all these secondary wavelets.
• The wavefront in a medium is always perpendicular to the direction of wave propagation.
• Secondary wavelets travel only in the forward direction — backward wavelets are ignored (zero amplitude in backward direction).

Memory: Every point → new source → envelope = new wavefront.

Reflection Using Huygens' Principle:

• Reflection is a sudden change in direction of propagation of a wave that strikes a boundary between two different media.
• If incoming rays are plane waves with infinite parallel planes, the wave AB falls on a reflecting surface and is incident perpendicular to the incident ray at angle i.
• AA₁ = BE (equal distances), triangles are congruent → ∠i = ∠r (angle of incidence = angle of reflection). ✓
• First Law of Reflection: ∠i = ∠r
• Second Law: Incident wavefront, reflected wavefront, and normal all lie in same plane perpendicular to reflecting surface.

Refraction Using Huygens' Principle:

• Refraction is the change in velocity of light as it passes from one medium to another.
• If a plane wavefront AB is incident on a surface, v₁ and v₂ are velocities in medium 1 and 2 respectively (v₁ > v₂).
• From Huygens' principle, A and C form the source of secondary spherical wavelets; time = t.

△ADC gives: \[\frac{\sin i}{\sin r}=\frac{\left(\frac{BC}{AC}\right)}{\left(\frac{AD}{AC}\right)}=\frac{BC}{AD}=\frac{v_{1}t}{v_{2}t}=\frac{v_{1}}{v_{2}}=\mu,\]

This proves Snell's Law of Refraction: \[\frac{\sin i}{\sin r}=\frac{v_{1}}{v_{2}}=n\mathrm{(constant)}\].

When light travels from optically rarer to denser medium obliquely:

• It bends towards the normal.
• Angle of incidence > angle of refraction.

Speed of light decreases in denser medium; frequency remains unchanged; wavelength decreases.

• Refractive index: \[\mu=\frac{c}{v},\] where c = speed of light in vacuum, v = speed in medium.

• Snell's law: \[\frac{\sin i}{\sin r}=\frac{\mu_2}{\mu_1}=\frac{v_1}{v_2}=\frac{\lambda_1}{\lambda_2}\]

When light travels from optically denser to rarer medium obliquely:

• It bends away from the normal.
• Angle of refraction > angle of incidence.

If angle of incidence exceeds the Critical Angle (C), total internal reflection occurs.

Critical Angle: \[C=\sin^{-1}\left(\frac{\mu_{2}}{\mu_{1}}\right),\mathrm{where~}\mu_{1}>\mu_{2}.\]

At critical angle, refracted ray grazes the surface (angle of refraction = 90°).

Laws of Reflection (proved by Huygens' principle):

• ∠i = ∠r (angle of incidence = angle of reflection)
• Incident ray, reflected ray, and normal all lie in the same plane.

Reflected wavefront is a plane wavefront (mirror image of incident wavefront).

No change in frequency, wavelength, or speed during reflection.

The wavefront after reflection from a plane surface remains planar.

Coherent Sources-

Two sources are coherent if they emit waves of:

• Same frequency
• Constant (fixed) phase difference
• Obtained from a single source

Two coherent sources can be created by:

• Splitting a physical source into two
• Generating two virtual images of the same source

Incoherent Sources-

• Phase difference changes with time → incoherent.
• Two independent monochromatic sources of same frequency are incoherent because atoms cannot emit light waves in same phase simultaneously.

Addition of Waves (Superposition)

Let two waves have amplitudes A₁ and A₂, same frequency, and constant phase difference φ.

• Resultant amplitude: \[A_{res}=\sqrt{A_1^2+A_2^2+2A_1A_2\cos\phi}\]

• Phase angle: \[\theta=\tan^{-1}\left(\frac{A_2\sin\phi}{A_1+A_2\cos\phi}\right)\]

• Since I ∝ A²: \[I=I_1+I_2+2\sqrt{I_1I_2}\cos\phi\]

• Interference = redistribution of energy when two coherent waves superpose.
• Based on energy conservation, total energy remains constant, only redistributed.
• Constructive: I > (I₁ + I₂) → bright fringe
• Destructive: I < (I₁ + I₂) → dark fringe

Conditions for Sustained Interference:

• Sources must be coherent.
• Separation between sources must be small.
• Distance of screen from sources must be large.
• For good contrast: amplitudes of the two waves should be nearly equal.
• Two sources must propagate along same line.

Young's Double Slit Experiment (YDSE):

Setup: Light source → single slit → double slit (S₁ and S₂, separation d) → screen (distance D).

Path difference at point P: \[\delta=S_2P-S_1P=\frac{x_n\cdot d}{D}\]

Bright Fringe (Constructive): Path difference = even multiple of λ/2

δ = nλ, n = 0,1,2,3...

Dark Fringe (Destructive): Path difference = odd multiple of λ/2

• Diffraction = bending and spreading of light waves around obstacles or through narrow openings, producing interference patterns.
• It is due to interference of secondary wavelets from the exposed portion of the wavefront from the slit.
• Key difference from interference: in diffraction, bright fringes have same intensity but bands are of decreasing intensity.

Single Slit Diffraction:

Let a = width of slit, θ = angle of diffraction.

Condition for Minimum (Dark) Intensity:

Condition for Maximum (Secondary Bright) Intensity:

\[a\sin\theta=(2n+1)\frac{\lambda}{2},\quad n=1,2,3...\]

Width of Central Maximum:

For first minima: \[a\cdot\frac{y}{D}=\lambda\Rightarrow y=\frac{\lambda D}{a}\]

\[W=2y=\frac{2\lambda D}{a}\]

Angular width of central maximum:

Linear width of n-th secondary maximum:

• 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.