PhysicsNCERT Class 12
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Ray Optics and Optical Instruments Notes

Study Notes

5 Topics27 Formulas9 PYQs36 Key Points

Topics

5
1

Chapter Overview

Overview

Ray optics studies light by treating it as straight-line rays. This approximation works when the size of obstacles, mirrors, lenses or apertures is much larger than the wavelength of light. The chapter begins with reflection by plane and spherical mirrors, then explains refraction using Snell’s law, refractive index, apparent depth, glass slabs and total internal reflection. Lenses extend refraction to image formation and optical power. Prisms explain deviation, minimum deviation and dispersion into a spectrum. Finally, optical instruments such as the human eye, microscope and telescope use mirrors and lenses to form useful magnified images. For NEET, sign convention, formula selection, ray diagrams and units are the most scoring parts.

Key Points6
  • 1Always draw the principal axis, pole or optical centre, focus and centre of curvature before solving image problems.
  • 2The refractive index of a medium is the ratio of speed of light in vacuum to speed in that medium.
  • 3Power of a lens depends on focal length in metres and is measured in dioptre.
  • 4Dispersion occurs because refractive index depends on wavelength; violet deviates more than red in ordinary glass.
  • 5The human eye forms a real, inverted image on the retina, but the brain interprets it upright.
  • 6Microscope is for nearby tiny objects; telescope is for distant objects.
Memory Tricks2

Chapter Order Trick

Remember M-R-L-P-I: Mirrors, Refraction, Lenses, Prism, Instruments. Most NEET problems combine only two adjacent blocks.

Formula Sign Alert

Mirror has plus between 1/v and 1/u; lens has minus before 1/u. Say: 'Mirror adds, Lens subtracts object.'

Examples1

Daily Life Map

Rear-view mirrors use convex mirrors, spectacles use lenses, diamonds shine due to total internal reflection, rainbows involve dispersion, and telescopes use lenses or mirrors to view distant objects.

Reference Tables2
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Common Mistakes2

Using Formula Without Sign Convention

Many wrong NEET answers come from substituting only magnitudes. Always assign signs to u, v, f and height before calculation.

Confusing Linear and Angular Magnification

Mirror and lens image size usually use linear magnification, while microscope and telescope use angular magnification.

Formula Cards4
Mirror Formula

Relates focal length, image distance and object distance for spherical mirrors using Cartesian sign convention.

Variables

f=

focal length of the mirror

v=

image distance from pole

u=

object distance from pole

Snell's Law

Gives bending of light at the interface of two transparent media.

Variables

n1, n2=

refractive indices of incident and refracting media

i=

angle of incidence

r=

angle of refraction

Diagrams3
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2

Reflection by Mirrors

Overview

Reflection occurs when light returns into the same medium after striking a surface. Plane mirrors form virtual, erect, laterally inverted images of the same size behind the mirror. Spherical mirrors are parts of a sphere: concave mirrors are converging and convex mirrors are diverging. Concave mirrors form different images depending on object position: real inverted images for objects beyond focus and virtual erect enlarged images when the object is between pole and focus. Convex mirrors always form virtual, erect and diminished images behind the mirror. NEET questions usually test ray diagrams, mirror formula, magnification, focal length-radius relation and correct Cartesian sign convention.

Key Points6
  • 1A ray parallel to principal axis reflects through focus for concave mirror and appears to come from focus for convex mirror.
  • 2A ray passing through centre of curvature retraces its path after reflection.
  • 3A ray incident at pole reflects symmetrically with respect to the principal axis.
  • 4Real images are formed in front of the mirror and are inverted.
  • 5Virtual images are formed behind the mirror and are erect.
  • 6The sign of magnification reveals image nature: negative means inverted, positive means erect.
Memory Tricks2

C-F-P Order

For a concave mirror facing left, remember from left to right: C, F, P. The focus is always halfway between centre and pole.

Convex Mirror Nature

Convex mirror = VIP image: Virtual, erect, diminished, behind the mirror. It is always safe for rear-view mirrors.

Examples2

Numerical Example

An object is 30 cm in front of a concave mirror of focal length 15 cm. Here u = -30 cm, f = -15 cm. From 1/f = 1/v + 1/u, 1/v = -1/15 + 1/30 = -1/30, so v = -30 cm. Image forms at C, real, inverted and same size.

Real-Life Example

A dentist uses a concave mirror close to the tooth because when the object is within focus, the image is virtual, erect and magnified.

Reference Tables2
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Common Mistakes3

Wrong Sign of Concave Mirror Focal Length

In NCERT Cartesian convention, a concave mirror has negative focal length because its focus lies in front of the mirror, opposite the positive direction.

Forgetting Minus in Magnification

Mirror magnification is m = -v/u, not v/u. The negative sign is essential for image orientation.

Calling All Concave Images Real

A concave mirror gives a virtual erect image when the object is between pole and focus.

Formula Cards3
Mirror Formula

Used for concave and convex spherical mirrors with Cartesian sign convention.

Variables

f=

focal length of mirror

v=

image distance from pole

u=

object distance from pole

Focal Length and Radius

The focus lies midway between pole and centre of curvature for paraxial rays.

Variables

f=

focal length

R=

radius of curvature

Diagrams4
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3

Refraction & Total Internal Reflection

Overview

Refraction is the bending of light when it passes obliquely from one transparent medium to another because its speed changes. Snell’s law connects angles of incidence and refraction with refractive indices. Refractive index measures optical density and equals c/v for a medium. Through a rectangular slab, the emergent ray is parallel to the incident ray but laterally displaced. When light travels from denser to rarer medium, refraction bends away from normal. At the critical angle, the refracted ray grazes the surface; for larger incidence angles, total internal reflection occurs. Optical fibres, mirages, diamond brilliance and endoscopy depend on total internal reflection.

Key Points6
  • 1Refractive index is dimensionless and is generally greater than 1 for transparent materials.
  • 2Frequency of light remains unchanged during refraction; speed and wavelength change.
  • 3In a glass slab, lateral shift increases with slab thickness and angle of incidence.
  • 4Critical angle exists only for light going from optically denser to optically rarer medium.
  • 5Optical fibre works by repeated total internal reflection inside a high-index core.
  • 6Total internal reflection is 100 percent reflection ideally, unlike ordinary reflection.
Memory Tricks2

Bending Rule

Slow medium pulls the ray towards normal. If light slows down, it bends towards normal; if it speeds up, it bends away.

TIR Rule

TIR = Dense to Rare + Bigger than Critical. Remember: 'DR and Big C-crossing gives TIR.'

Examples2

Critical Angle Example

For glass of refractive index 1.5 to air, sin C = 1/1.5 = 2/3. Thus C ≈ 41.8°. If incidence angle inside glass is 50°, total internal reflection occurs.

Apparent Depth Example

A coin at the bottom of water appears raised because rays bend away from normal while emerging from water to air. If water depth is 12 cm and n = 4/3, apparent depth is 9 cm.

Reference Tables2
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Common Mistakes3

Assuming TIR Can Occur From Air to Glass

Total internal reflection cannot occur from rarer to denser medium. It needs denser to rarer travel.

Changing Frequency During Refraction

Frequency remains constant at a boundary. Speed and wavelength change according to the medium.

Using sin C = n1/n2 Incorrectly

For denser n1 to rarer n2, sin C = n2/n1. The ratio must be less than or equal to 1.

Formula Cards5
Absolute Refractive Index

Defines refractive index of a medium relative to vacuum.

Variables

n=

absolute refractive index

c=

speed of light in vacuum

v=

speed of light in the medium

Relative Refractive Index

Refractive index of medium 2 with respect to medium 1.

Variables

n21=

refractive index of medium 2 relative to medium 1

n1, n2=

absolute refractive indices

v1, v2=

speeds of light in media 1 and 2

Snell's Law

Connects direction change of light to refractive indices of two media.

Variables

n1=

refractive index of incident medium

n2=

refractive index of refracting medium

i=

angle of incidence

r=

angle of refraction

Diagrams5
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4

Lenses

Overview

A lens forms images by refraction at its two spherical surfaces. A convex lens is thicker at the centre and converges paraxial rays to a real focus, so its focal length and power are positive. A concave lens is thinner at the centre and diverges rays as if they come from a virtual focus, so its focal length and power are negative. Thin lens formula connects object distance, image distance and focal length. Magnification gives image size and orientation. Lens power is especially important in spectacles and combinations. In contact, powers add algebraically, making lens combination questions quick and highly scoring in NEET.

Key Points6
  • 1A ray parallel to the principal axis passes through focus after refraction by a convex lens.
  • 2A ray through optical centre of a thin lens passes undeviated approximately.
  • 3A ray through focus before a convex lens emerges parallel to the principal axis.
  • 4Real images by lenses form on the opposite side of the object and are usually inverted.
  • 5Virtual images by lenses form on the same side as the object and are erect.
  • 6Power must be calculated using focal length in metres, not centimetres.
Memory Tricks2

Lens Sign Trick

Convex lens can collect light, so it has positive focal length and positive power. Concave lens spreads light, so its focal length and power are negative.

Power Unit Trick

Dioptre demands metre. Before P = 1/f, convert cm to m. A 25 cm lens is not 1/25 D; it is 1/0.25 = 4 D.

Examples2

Lens Numerical Example

A convex lens has f = +20 cm and object distance u = -30 cm. Using 1/f = 1/v - 1/u: 1/20 = 1/v + 1/30, so 1/v = 1/20 - 1/30 = 1/60. Thus v = +60 cm. Image is real, inverted and magnified.

Power Example

A lens of focal length -50 cm has f = -0.50 m, so P = 1/(-0.50) = -2 D. It is a concave lens used for myopia correction.

Reference Tables3
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Common Mistakes3

Using Mirror Magnification for Lenses

For lenses, m = v/u. The mirror formula has m = -v/u. Mixing these gives wrong orientation.

Adding Focal Lengths Instead of Powers

For lenses in contact, powers add algebraically. Focal lengths do not simply add.

Ignoring Negative Power

Concave lens power is negative. In spectacle problems, the sign tells whether myopia or hypermetropia is corrected.

Formula Cards5
Thin Lens Formula

Relates focal length, object distance and image distance for a thin lens.

Variables

f=

focal length of lens

v=

image distance from optical centre

u=

object distance from optical centre

Lens Magnification

Determines size and orientation of image formed by a lens.

Variables

m=

linear magnification

h'=

height of image

h=

height of object

v=

image distance

u=

object distance

Power of Lens

Power is measured in dioptre when focal length is in metre.

Variables

P=

power of lens in dioptre

f=

focal length in metre

Diagrams4
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5

Prism

Overview

A prism refracts light at two inclined surfaces, so the emergent ray is deviated from the incident direction. The angle between the incident ray produced and emergent ray produced is called angle of deviation. As angle of incidence changes, deviation first decreases, reaches a minimum and then increases. At minimum deviation, the ray path is symmetric inside the prism, meaning i = e and r1 = r2 = A/2. White light splits into colours because refractive index depends on wavelength. Violet light has higher refractive index and deviates more, while red deviates least. NEET commonly asks formulas for minimum deviation, dispersion order and spectrum formation.

Key Points6
  • 1Deviation depends on angle of incidence, prism angle and refractive index.
  • 2Minimum deviation occurs when the ray travels symmetrically through the prism.
  • 3Dispersion is splitting of white light into constituent colours due to wavelength-dependent refractive index.
  • 4Angular dispersion is the angle between emergent violet and red rays.
  • 5Mean deviation is often considered for yellow light in prism problems.
  • 6A prism bends light towards its base.
Memory Tricks2

Spectrum Order

VIBGYOR from maximum deviation to minimum deviation in a glass prism. Violet bends most; Red bends least.

Minimum Deviation Symmetry

At Dm, the ray behaves like a mirror-symmetric path: i = e and r1 = r2.

Examples2

Minimum Deviation Example

For an equilateral prism A = 60° and Dm = 40°, n = sin[(60° + 40°)/2]/sin(60°/2) = sin50°/sin30° = 0.766/0.5 ≈ 1.53.

Real-Life Example

A glass prism spreads sunlight into a coloured spectrum. This is similar to how raindrops disperse sunlight to form a rainbow.

Reference Tables2
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Common Mistakes3

Reversing Red and Violet Deviation

In ordinary glass, violet has greater refractive index and deviates more. Red deviates least.

Using Degrees in Small Angle Formula Without Care

The thin prism formula δ ≈ (n - 1)A is safest when angles are small and expressed consistently, usually in radians for calculation.

Forgetting A = r1 + r2

This relation is central to prism geometry and is often needed before applying deviation formula.

Formula Cards4
Prism Angle Relation

In a prism, the prism angle equals the sum of the two refraction angles inside the prism.

Variables

A=

angle of prism

r1=

angle of refraction at first face

r2=

angle of incidence at second face inside prism

Angle of Deviation

Gives deviation produced by a prism for any ray path.

Variables

δ=

angle of deviation

i=

angle of incidence at first face

e=

angle of emergence at second face

A=

angle of prism

Diagrams4
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6

Optical Instruments

Overview

Optical instruments use lenses and mirrors to increase visual ability. The human eye has a convex eye lens that forms a real image on the retina. Accommodation changes focal length to focus near and far objects. Myopia is corrected by a concave lens, while hypermetropia and presbyopia are corrected using convex lenses or bifocals as needed. A simple microscope uses a convex lens to increase angular size. A compound microscope uses objective and eyepiece lenses to produce large magnification of tiny nearby objects. An astronomical telescope uses a large focal length objective and short focal length eyepiece to view distant objects. Resolving power describes ability to distinguish close objects.

Key Points6
  • 1The retina acts as the screen where a real, inverted image is formed.
  • 2Accommodation is the ability of the eye lens to change focal length using ciliary muscles.
  • 3Microscope needs a short focal length objective for high magnification.
  • 4Telescope needs a large aperture objective to collect more light and improve resolution.
  • 5In normal adjustment of telescope, final image is at infinity, reducing eye strain.
  • 6Resolving power improves when aperture increases and wavelength decreases.
Memory Tricks3

Vision Defect Correction

Myopia uses Minus lens: both start with M. Hypermetropia needs Plus lens: think Hyper people need extra positive help for near vision.

Telescope Design

Telescope objective is 'FAT': Focal length large, Aperture large, for distant Targets.

Microscope Design

Microscope needs tiny focal lengths because it studies tiny objects. Small f gives large magnification.

Examples3

Spectacle Example

A person needs a lens of power -2 D. Since power is negative, the lens is concave and corrects myopia. Its focal length is f = 1/P = -0.5 m.

Telescope Example

If a telescope has objective focal length 100 cm and eyepiece focal length 5 cm, magnifying power in normal adjustment is M = fo/fe = 100/5 = 20.

Microscope Example

A simple microscope of focal length 5 cm gives magnification M = 1 + D/f = 1 + 25/5 = 6 when final image is at the near point.

Reference Tables3
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Common Mistakes4

Confusing Myopia and Hypermetropia

Myopia is near-sightedness: near objects clear, distant objects blurred. Hypermetropia is far-sightedness: distant objects clear, nearby objects blurred.

Using Linear Magnification for Telescope

Telescope magnification is angular magnification because objects are very far away and actual image size is not the main comparison.

Wrong Telescope Objective

The objective of a telescope should have large focal length and large aperture, not small focal length.

Ignoring Relaxed Eye Condition

Final image at infinity is called normal adjustment and is more comfortable because the eye is relaxed.

Formula Cards6
Simple Microscope Magnification for Final Image at Near Point

Angular magnification when final image is formed at the least distance of distinct vision.

Variables

M=

angular magnification

D=

least distance of distinct vision, about 25 cm

f=

focal length of magnifying lens

Simple Microscope Magnification for Relaxed Eye

Angular magnification when final image is at infinity.

Variables

M=

angular magnification

D=

least distance of distinct vision

f=

focal length of lens

Compound Microscope Magnification

Approximate magnification in normal adjustment.

Variables

M=

total magnification

L=

tube length

fo=

focal length of objective

fe=

focal length of eyepiece

D=

least distance of distinct vision

Diagrams6
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Formula Sheet

10
Mirror Formula

Relates focal length, image distance and object distance for spherical mirrors using Cartesian sign convention.

Variables

f=

focal length of the mirror

v=

image distance from pole

u=

object distance from pole

Snell's Law

Gives bending of light at the interface of two transparent media.

Variables

n1, n2=

refractive indices of incident and refracting media

i=

angle of incidence

r=

angle of refraction

Lens Formula

Relates focal length, image distance and object distance for thin lenses.

Variables

f=

focal length of lens

v=

image distance from optical centre

u=

object distance from optical centre

Power of Lens

Power is the ability of a lens to converge or diverge light; focal length must be in metres.

Variables

P=

power in dioptre

f=

focal length in metre

Mirror Formula

Used for concave and convex spherical mirrors with Cartesian sign convention.

Variables

f=

focal length of mirror

v=

image distance from pole

u=

object distance from pole

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NEET PYQs — Ray Optics and Optical Instruments

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NEET 2021Set P3HardQ1

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror is kept perpendicular to the principal axis and at a distance of 40 cm from the lens, the final image would be formed at a distance of:

NEET 2021Set P3MediumQ2

A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance d between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then 'd' is:

NEET 2021Set P3EasyQ3

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since

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