Class 12 Physics · NCERT chapter 9 · 10 topics · free to read
Reflection at Spherical Mirrors
Spherical mirrors (concave & convex) form images by reflecting light following the mirror formula 1/v + 1/u = 1/f. Sign convention is the key to getting numericals right — one wrong sign and real becomes virtual.
1 v + 1 u = 1 f
Sign Convention
The Cartesian sign convention assigns positive/negative signs to distances measured from the pole of the mirror. Master this first — every formula depends on it.
The New Cartesian Sign Convention uses the pole (P) of the mirror as the origin. All distances are measured from the pole along the principal axis.
All distances measured from the pole (P) of the mirror
Distances in the direction of incident light → positive (conventionally left to right)
Distances against incident light → negative (right to left, toward the mirror)
Object distance u is always negative (object is always on the left of the mirror)
Heights above the principal axis → positive; below → negative
Focal length: concave mirror → f < 0 , convex mirror → f > 0
Concave Mirror
A concave mirror converges parallel rays to a real focus. It can form real or virtual images depending on where the object is placed relative to the focus.
A concave mirror has its reflecting surface curved inward (like the inside of a spoon). Parallel rays converge to a real focus F in front of the mirror. The focal length f = R/2 , where R is the radius of curvature.
Object at infinity → image at F (real, inverted, highly diminished) — used in solar cookers
Object beyond C → image between F and C (real, inverted, diminished)
Object at C → image at C (real, inverted, same size)
Object between C and F → image beyond C (real, inverted, magnified)
Object at F → image at infinity (real, inverted, highly magnified)
Object between F and P → image behind mirror (virtual, erect, magnified) — shaving mirror setup
Convex Mirror
A convex mirror diverges light and always forms virtual, erect, diminished images regardless of object position. That's why it's used as a rear-view mirror.
A convex mirror has its reflecting surface curved outward (like the back of a spoon). Parallel rays diverge after reflection, but appear to come from a virtual focus F behind the mirror. The focal length is positive ( f > 0 ).
Image is always virtual, erect, and diminished — no exceptions
Image forms between P and F (behind the mirror)
As object moves from infinity to the mirror: image moves from F toward P, growing in size (but never reaching actual size)
Wider field of view than plane mirrors → used for security and vehicle mirrors
Focal length: f = +R/2 (positive by sign convention)
Converging mirror
Diverging mirror
f < 0 (real focus in front)
f > 0 (virtual focus behind)
Can form real AND virtual images
Only virtual images
Image can be magnified or diminished
Image is always diminished
Used: headlights, solar cookers, dentist mirror
Used: rear-view mirror, ATM security mirror
Mirror Formula & Magnification
The mirror formula relates object distance, image distance, and focal length. Magnification tells you image size and orientation.
1 v + 1 u = 1 f
This is the mirror formula, valid for both concave and convex mirrors (with proper sign convention). Here u = object distance, v = image distance, f = focal length, all measured from the pole.
m = h_i h_o = - v u
Magnification m is the ratio of image height to object height. The negative sign means: if v and u have the same sign → m < 0 → inverted image (real). If opposite signs → m > 0 → erect image (virtual).
m > 0 : image is erect (virtual for mirrors)
m < 0 : image is inverted (real for mirrors)
|m| > 1 : image is magnified
|m| < 1 : image is diminished
|m| = 1 : image is same size as object (object at C for concave mirror)
Relation: f = R/2 — always, for any spherical mirror
Quick recall
A concave mirror has focal length 15 cm. An object is placed 30 cm from it. Find the image position and magnification.
Using sign convention: u = -30 cm, f = -15 cm. Mirror formula: 1 v + 1 -30 = 1 -15 → 1 v = - 1 15 + 1 30 = - 1 30 → v = -30 cm. Magnification: m = -v/u = -(-30)/(-30) = -1 . Image is at C (30 cm in front), real, inverted, same size.
Refraction & Snell's Law
When light crosses the boundary between two media, it bends. Snell's law (n₁ sin θ₁ = n₂ sin θ₂) quantifies exactly how much. Refractive index is the key property — it tells you how 'optically dense' a medium is.
n_1 _1 = n_2 _2
Refraction
When light passes from one transparent medium to another, it changes direction at the boundary. The bending happens because light travels at different speeds in different media.
Refraction is the change in direction of light when it passes from one transparent medium to another. This happens because the speed of light is different in different media. Light bends toward the normal when entering a denser medium, and away from the normal when entering a rarer medium.
Denser medium → light slows down → bends toward normal ( _2 < _1 )
Rarer medium → light speeds up → bends away from normal ( _2 > _1 )
At normal incidence ( _1 = 0° ) → no bending, light goes straight through
Frequency of light does NOT change during refraction — only wavelength and speed change
The incident ray, refracted ray, and normal all lie in the same plane
Snell's Law
Snell's law relates the angles of incidence and refraction to the refractive indices of the two media. It's the fundamental equation of refraction.
n_1 _1 = n_2 _2
Here n_1 and n_2 are the refractive indices of medium 1 (incident) and medium 2 (refracted), and _1 , _2 are the angles of incidence and refraction measured from the normal.
The refractive index of a medium is the ratio of the speed of light in vacuum to the speed in that medium:
n = c v
n is always 1 (light is fastest in vacuum where n = 1 )
Water: n = 1.33 , Glass: n 1.5 , Diamond: n = 2.42
Higher n → denser medium → light travels slower → bends more toward normal
n_ 21 = 1 n_ 12 — relative indices are reciprocals of each other
Real & Apparent Depth
An object under water appears closer to the surface than it actually is. The ratio of real to apparent depth equals the refractive index.
Apparent depth = Real depth n
When you look at an object submerged in a denser medium (like a coin at the bottom of a pool), light rays from the object bend away from the normal as they exit into air. Your brain traces the refracted rays backward in straight lines, placing the image closer to the surface.
Viewing from rarer medium into denser medium → object appears closer (apparent depth < real depth)
Viewing from denser medium into rarer medium → object appears farther
Formula only valid for near-normal viewing (looking almost straight down)
Shift = Real depth (1 - 1/n) — this is the apparent upward shift of the object
Quick recall
A tank has water ( n = 4/3 ) on top and a glass slab ( n = 3/2 ) at the bottom. Water depth = 20 cm, glass thickness = 10 cm. What is the apparent depth of the bottom of the glass?
Apparent depth of glass = 10/(3/2) = 6.67 cm. Apparent depth of water above = 20/(4/3) = 15 cm. Total apparent depth = 6.67 + 15 = 21.67 cm (actual total = 30 cm). Each layer is treated independently — divide real depth by that medium's refractive index.
Total Internal Reflection
When light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle, the light is completely reflected back — no refraction occurs. This is why diamonds sparkle, optical fibers work, and mirages form.
_c = n_2 n_1 (n_1 > n_2)
Critical Angle
The critical angle is the angle of incidence in the denser medium for which the refracted ray grazes along the boundary (angle of refraction = 90°). Beyond this angle, total internal reflection occurs.
When light goes from a denser medium ( n_1 ) to a rarer medium ( n_2 , where n_1 > n_2 ), the refracted ray bends away from the normal. As you increase the angle of incidence, the refracted ray bends further away. At a specific angle called the critical angle _c , the refracted ray travels along the boundary ( _2 = 90° ).
n_1 _c = n_2 90° _c = n_2 n_1
Critical angle exists ONLY when light goes from denser to rarer medium ( n_1 > n_2 )
At _i = _c : refracted ray grazes the surface ( _r = 90° )
At _i > _c : NO refraction — 100% of light is reflected back
Critical angle for water-air: _c 48.6°
Critical angle for glass-air: _c 42°
Critical angle for diamond-air: _c 24.4° — very small, so TIR happens easily
Applications of TIR
Total internal reflection isn't just a textbook concept — it powers the internet (optical fibers), makes diamonds sparkle, creates mirages on hot roads, and enables totally reflecting prisms.
TIR has remarkable real-world applications because it provides 100% reflection with zero absorption losses — no mirror can match this.
Optical fibers: Light enters a glass core and undergoes repeated TIR at the core-cladding boundary, traveling kilometers without loss. The core has higher n than the cladding
Diamond cutting: Diamonds are cut to maximize TIR inside the stone. Light enters the top, undergoes multiple TIR at the angled facets, and exits back through the top → brilliant sparkle
Mirages: Hot road surface heats the air above it, creating layers of decreasing n near the ground. Light from the sky curves downward and undergoes TIR → you see a 'puddle' (sky reflection) on the road
Totally reflecting prisms: A 45-90-45° glass prism reflects light by 90° or 180° using TIR. Better than mirrors because there's no energy loss (prisms in periscopes and binoculars)
Endoscopy: Optical fiber bundles allow doctors to see inside the body without surgery
100% of light reflected — zero loss
Some light absorbed — always < 100%
Needs denser-to-rarer boundary
Works at any surface
Only above critical angle
Works at all angles
Used in prisms, fibers, diamonds
Used in mirrors, telescopes
No metallic coating needed
Requires reflective coating
Refraction at Spherical Surfaces
When light refracts at a single curved boundary between two media, we get a formula relating object distance, image distance, refractive indices, and radius of curvature. This is the stepping stone to deriving the lens maker's equation.
n_2 v - n_1 u = n_2 - n_1 R
Refraction at a Single Spherical Surface
The formula for refraction at a single curved boundary between two different media. This is more fundamental than the lens formula — lenses are just two of these surfaces back-to-back.
When light passes from medium 1 (refractive index n_1 ) to medium 2 (refractive index n_2 ) through a spherical boundary of radius R , the object distance u , image distance v , and the properties of both media are related by:
n_2 v - n_1 u = n_2 - n_1 R
All distances measured from the center of the spherical surface (not from the lens center)
Sign convention: same Cartesian convention — distances along incident light positive, against it negative
R > 0 if center of curvature is on the refracted-light side; R < 0 if on the incident-light side
For a flat surface ( R = ): formula simplifies to n_2 v = n_1 u → gives real/apparent depth
This formula is valid for paraxial rays only (small aperture assumption)
Magnification at Spherical Surfaces
When light refracts at a spherical surface, the image size differs from the object size. The magnification depends on both the distances and the refractive indices.
m = h_i h_o = n_1 v n_2 u
Unlike mirrors, the magnification for refraction at a spherical surface involves the refractive indices. This is because the lateral magnification depends on Snell's law at the curved boundary.
m > 0 → erect image; m < 0 → inverted image
|m| > 1 → magnified; |m| < 1 → diminished
Note the difference from mirror magnification ( m = -v/u ) — here the n values are involved
For a plane surface ( R ): lateral magnification = 1 (image is same size but shifted in depth)
Quick recall
A convex surface of radius 20 cm separates air ( n_1 = 1 ) from glass ( n_2 = 1.5 ). Object is 30 cm from the surface in air. Find image position.
Using n_2 v - n_1 u = n_2 - n_1 R : 1.5 v - 1 -30 = 1.5 - 1 +20 . So 1.5 v + 1 30 = 0.5 20 = 1 40 . 1.5 v = 1 40 - 1 30 = 3-4 120 = - 1 120 . v = -180 cm. Negative v → image is on the same side as the object (virtual image in air).
Thin Lenses
The lens formula (1/v - 1/u = 1/f), lens maker's equation, and power of a lens are the backbone of geometric optics. Convex lenses converge light, concave lenses diverge it. Combining lenses? Just add their powers.
1 v - 1 u = 1 f
Lens Formula
The thin lens formula relates object distance, image distance, and focal length for any thin lens. Note the minus sign difference from the mirror formula.
1 v - 1 u = 1 f
For a thin lens, all distances are measured from the optical center (O). The sign convention is identical to mirrors: distances along incident light are positive, against are negative.
Convex (converging) lens: f > 0 — positive focal length
Concave (diverging) lens: f < 0 — negative focal length
Object distance u : always negative (object on left)
If v > 0 : real image (on opposite side from object)
If v < 0 : virtual image (on same side as object)
Magnification: m = v u (no minus sign, unlike mirrors)
Converging — brings rays together
Diverging — spreads rays apart
f > 0 (positive focal length)
f < 0 (negative focal length)
Can form real AND virtual images
ONLY virtual images (for real objects)
Used: magnifying glass, camera, eye
Used: correcting myopia, peephole
Thicker at center, thinner at edges
Thinner at center, thicker at edges
Lens Maker's Equation
The lens maker's equation tells you the focal length of a lens based on its refractive index and the radii of curvature of its two surfaces. It's how lens designers engineer specific focal lengths.
1 f = (n - 1) ( 1 R_1 - 1 R_2 )
Here n is the refractive index of the lens material (relative to the surrounding medium), R_1 is the radius of curvature of the first surface (facing the object), and R_2 is the radius of the second surface.
n = refractive index of lens relative to surrounding medium
For a biconvex lens: R_1 > 0 (center of curvature on right), R_2 < 0 (center on left) → f > 0
For a biconcave lens: R_1 < 0 , R_2 > 0 → f < 0
Plano-convex: one flat side ( R = ), one convex → 1 f = (n-1)/R
If the lens is in a medium with n_ medium > n_ lens : a convex lens acts as diverging!
Power of a Lens & Combination
Power measures how strongly a lens converges or diverges light. For thin lenses in contact, powers simply add up — making lens design elegant.
P = 1 f (in metres) Unit: dioptre (D)
Power of a lens is the reciprocal of its focal length in metres. A lens with f = +50 cm ( = 0.5 m) has P = +2 D. Positive power → converging. Negative power → diverging.
For two thin lenses in contact, the combined power is simply the sum of individual powers:
For lenses in contact: P = P_1 + P_2 + P_3 + — just add
This works because thin lenses in contact act as a single equivalent lens
A convex + concave combination: if |P_ convex | > |P_ concave | → net converging
Quick recall
A convex lens of power +5 D is placed in contact with a concave lens of power -3 D. What is the focal length of the combination?
P = P_1 + P_2 = +5 + (-3) = +2 D. Focal length f = 1/P = 1/2 = 0.5 m = 50 cm. The combination acts as a converging lens of focal length 50 cm.
Refraction Through Prism
A prism bends light and splits white light into its constituent colors (dispersion). The deviation depends on the angle of incidence and the prism angle. At minimum deviation, the ray passes symmetrically through the prism.
n = ( A + D_m 2 ) ( A 2 )
Deviation by a Prism
When light enters a prism, it refracts at both surfaces. The total deviation (angle between incident and emergent rays) depends on the prism angle, refractive index, and angle of incidence.
A prism is a transparent optical element with flat, polished surfaces at an angle. The angle between the two refracting surfaces is the prism angle A (also called the angle of the prism). When a ray enters and exits, the total angle of deviation is the angle between the original incident ray and the final emergent ray.
= (i_1 + i_2) - A
Here i_1 = angle of incidence at the first surface, i_2 = angle of emergence at the second surface, and A = prism angle. Also, r_1 + r_2 = A , where r_1 and r_2 are the angles of refraction inside the prism.
Light always bends toward the base of the prism
Total deviation = i_1 + i_2 - A
Inside the prism: r_1 + r_2 = A (geometry of the prism)
At each surface, Snell's law applies: n_1 i = n_2 r
As i_1 increases from grazing, first decreases, reaches a minimum, then increases — a U-shaped curve
Minimum Deviation
At minimum deviation, the ray passes symmetrically through the prism (i₁ = i₂, r₁ = r₂). This special condition gives us the cleanest formula for refractive index.
As you vary the angle of incidence, the deviation first decreases and then increases. At the minimum deviation D_m , the ray inside the prism is parallel to the base. This is the symmetric configuration where i_1 = i_2 and r_1 = r_2 = A/2 .
n = ( A + D_m 2 ) ( A 2 )
Minimum deviation occurs when the ray passes symmetrically through the prism
At D_m : i_1 = i_2 (angle of incidence = angle of emergence)
A prism splits white light into a spectrum (VIBGYOR) because the refractive index depends on wavelength — violet bends most, red bends least.
Dispersion is the splitting of white light into its constituent wavelengths (colors) by a prism. This happens because the refractive index of a material depends on the wavelength of light — shorter wavelengths (violet) have higher n and bend more than longer wavelengths (red).
Spectrum order: VIBGYOR — Violet (most deviated) to Red (least deviated)
Violet: n 1.532 , Red: n 1.514 (for crown glass) — small difference, big effect
Cauchy's equation: n = A + B ^2 — n increases as decreases
Angular dispersion = _V - _R — the angular spread between violet and red
Can occur without dispersion (if n is same for all )
Cannot occur without deviation
Minimized by achromatic combination
Eliminated by achromatic doublet
Optical Instruments: Eye
The human eye is the most remarkable optical instrument — a convex lens that adjusts its focal length in real time (accommodation). When it can't adjust enough, we get myopia, hypermetropia, or presbyopia, each corrected by a specific lens.
P = 1 f (corrective lens power in dioptres)
The Human Eye
The eye's crystalline lens changes shape to focus objects at different distances onto the retina. This ability to change focal length is called accommodation.
The human eye focuses light primarily through the cornea (fixed refractive power ~40 D) and the crystalline lens (adjustable, 18-24 D). The combined system forms a real, inverted, diminished image on the retina. Ciliary muscles change the curvature of the lens to focus on objects at different distances — this is accommodation.
Near point (D): closest distance of clear vision = 25 cm for a normal eye
Far point: farthest distance of clear vision = infinity for a normal eye
Range of accommodation: the range of focal length adjustment the lens can make
When looking at distant objects: ciliary muscles relax → lens becomes thin → f increases
When looking at nearby objects: ciliary muscles contract → lens becomes thick → f decreases
Retina has rods (dim light, no color) and cones (bright light, color vision)
The retinal image is actually inverted — your brain flips it right-side-up in real time. Experiments with inversion goggles show the brain can even adapt to permanently flipped vision within a few days!
Myopia (Short-Sightedness)
In myopia, the eyeball is too long or the lens too powerful, so distant objects focus in front of the retina. Corrected by a concave (diverging) lens.
Myopia (near-sightedness): the person can see nearby objects clearly but distant objects appear blurred. The image of distant objects forms in front of the retina instead of on it.
Cause: eyeball too long OR cornea/lens too curved (too much converging power)
Far point: not at infinity but at some finite distance (say, 2 m)
Correction: concave (diverging) lens — diverges light slightly before it enters the eye, pushing the image back onto the retina
Power of corrective lens: P = 1 f where f = - (far point distance)
Example: far point at 2 m → need lens with f = -2 m → P = -0.5 D
Hypermetropia & Presbyopia
In hypermetropia, the eyeball is too short or the lens too weak, so nearby objects focus behind the retina. Presbyopia is the age-related version. Both corrected by convex lenses.
Hypermetropia (far-sightedness): the person can see distant objects clearly but nearby objects appear blurred. The image of nearby objects forms behind the retina.
Cause: eyeball too short OR lens too flat (too little converging power)
Near point: farther than 25 cm (say, 50 cm or more)
Correction: convex (converging) lens — adds extra converging power to bring image forward onto retina
Presbyopia: same symptoms but caused by aging — ciliary muscles weaken, lens becomes rigid, can't accommodate for near objects
Presbyopia often needs bifocal lenses — upper part for distance (concave or plain), lower part for reading (convex)
Can't see far objects clearly
Can't see near objects clearly
Image forms in front of retina
Image forms behind retina
Eyeball too long / lens too strong
Eyeball too short / lens too weak
Corrected by concave (−) lens
Corrected by convex (+) lens
Far point < infinity
Near point > 25 cm
Quick recall
A hypermetropic person has near point at 75 cm. What corrective lens is needed to read at 25 cm?
The lens must form a virtual image at 75 cm when the object is at 25 cm. u = -25 cm, v = -75 cm (virtual, same side as object). Lens formula: 1 f = 1 -75 - 1 -25 = - 1 75 + 1 25 = 2 75 . f = 37.5 cm = 0.375 m. Power = +2.67 D (convex lens).
Simple Microscope & Compound Microscope
A simple microscope (magnifying glass) uses a single convex lens. A compound microscope uses two lenses — the objective creates a real magnified image, and the eyepiece magnifies it further. Total magnification = objective magnification x eyepiece magnification.
m = m_o m_e = L f_o D f_e
Simple Microscope
A single convex lens held close to the eye. The object is placed within the focal length to produce a virtual, erect, magnified image. Magnifying power depends on focal length and the least distance of distinct vision.
A simple microscope is a convex lens of short focal length. The object is placed between the lens and its focus, producing a virtual, erect, magnified image.
m = 1 + D f (image at near point, D = 25 cm)
m = D f (image at infinity — relaxed eye)
Object placed between F and the lens → virtual, erect, magnified image
Image at near point (D = 25 cm): m = 1 + D/f — maximum magnification, eye is strained
Image at infinity: m = D/f — slightly less magnification, but relaxed eye (comfortable viewing)
Smaller focal length → higher magnification
Practical limit: f few cm → m 5-10 ; beyond this, aberrations ruin the image
Compound Microscope
A compound microscope uses an objective lens (short focal length) to create a real magnified image, which the eyepiece (another short focal length lens) then magnifies further. Total magnification can reach 1000x or more.
A compound microscope has two convex lenses: the objective (short f_o , close to the object) and the eyepiece (short f_e , close to the eye). The objective forms a real, inverted, magnified intermediate image. The eyepiece acts as a simple microscope on this intermediate image.
m = m_o m_e = L f_o D f_e (image at infinity)
m = m_o m_e = L f_o (1 + D f_e ) (image at near point)
Here L = length of the microscope tube (distance between the two lenses, approximately), f_o = focal length of objective, f_e = focal length of eyepiece, D = 25 cm.
Object placed just beyond f_o → objective forms a real, magnified, inverted image
This intermediate image falls within f_e → eyepiece forms a virtual, magnified image
Final image is inverted (real image by objective is already inverted, eyepiece keeps it inverted)
Both f_o and f_e should be small for high magnification
f_o < f_e typically — the objective has the shorter focal length
Tube length L is measured between F_o' (back focus of objective) and F_e (front focus of eyepiece)
Quick recall
A compound microscope has f_o = 1 cm, f_e = 5 cm, tube length L = 20 cm. Find magnification for normal adjustment.
Normal adjustment means image at infinity. m = L f_o D f_e = 20 1 25 5 = 20 5 = 100 . The microscope magnifies 100 times.
Telescopes
Telescopes make distant objects appear closer by increasing their angular size. The refracting telescope uses two lenses (objective with large f, eyepiece with small f). Reflecting telescopes use mirrors to avoid chromatic aberration and can be made much larger.
m = f_o f_e
Astronomical Refracting Telescope
The astronomical telescope uses a large focal length objective to form a real image of a distant object, and a short focal length eyepiece to magnify that image. The final image is inverted.
An astronomical telescope (refracting type) consists of two convex lenses: a large-aperture, long focal length objective and a small, short focal length eyepiece. Light from a distant object is nearly parallel, so the objective forms a real image at its focus. The eyepiece magnifies this image.
m = f_o f_e (normal adjustment — image at infinity)
m = f_o f_e (1 + f_e D ) (image at near point)
Tube length (normal adjustment) = f_o + f_e
Objective: large f_o , large aperture (to collect more light from faint objects)
Eyepiece: small f_e (to magnify the intermediate image)
Magnification = f_o / f_e — large f_o and small f_e give high magnification
Tube length in normal adjustment: L = f_o + f_e
Final image is inverted — acceptable for astronomy (stars look the same upside down!)
For terrestrial use, a third erecting lens is added to make the image upright
Objective: large f_o
Objective: small f_o
Eyepiece: small f_e
Eyepiece: small f_e
m = f_o / f_e
m = (L/f_o)(D/f_e)
Object at infinity
Object very close to objective
Large aperture for light gathering
Large m for seeing tiny objects
f_o > f_e
f_o < f_e
Reflecting Telescope
Reflecting telescopes use a concave mirror as the objective instead of a lens. This eliminates chromatic aberration, allows much larger apertures, and is lighter and cheaper for the same size.
A reflecting telescope (Newtonian type) uses a large concave (parabolic) mirror as the objective to gather and focus light. A small plane mirror (at 45°) deflects the focused beam to a side-mounted eyepiece.
No chromatic aberration — mirrors reflect all wavelengths equally, unlike lenses which refract different colors differently
Large aperture possible — mirrors can be supported from behind; lenses can only be held at the edges and sag under their own weight
Lighter and cheaper — a mirror uses only one polished surface; a lens needs two precisely shaped surfaces of expensive glass
Less spherical aberration — parabolic mirrors eliminate spherical aberration completely
Most professional telescopes are reflectors (Hubble, James Webb Space Telescope)
Cassegrain telescope: uses a convex secondary mirror to fold the light path back through a hole in the primary mirror
Objective: convex lens
Objective: concave (parabolic) mirror
Has chromatic aberration
NO chromatic aberration
Limited aperture (lens sag)
Very large apertures possible
Heavier and more expensive
Lighter and cheaper for same size
Has spherical aberration
Parabolic mirror eliminates it
Longer tube length
Can be folded (Cassegrain design)
Scattering of Light
When light interacts with small particles, it gets scattered. Rayleigh scattering (intensity proportional to 1/lambda^4) explains why the sky is blue, sunsets are red, and the sea appears blue. The Tyndall effect makes light beams visible in dusty rooms.
I 1 ^4
Rayleigh Scattering
When light interacts with particles much smaller than its wavelength (like air molecules), shorter wavelengths scatter much more intensely. This wavelength-dependent scattering is called Rayleigh scattering.
Rayleigh scattering occurs when light interacts with particles much smaller than the wavelength of light (like N _2 and O _2 molecules, ~0.2 nm vs light at ~500 nm). The intensity of scattered light is inversely proportional to the fourth power of wavelength.
I_ scattered 1 ^4
Blue sky: Sunlight entering the atmosphere scatters in all directions. Blue/violet scatter most ( 1/ ^4 ). We see blue (not violet) because our eyes are more sensitive to blue and because sunlight has less violet to begin with
Red sunset/sunrise: At sunset, light travels through much more atmosphere. Blue is almost completely scattered away. Only red/orange light survives to reach your eyes directly → red sky
White clouds: Water droplets in clouds are much LARGER than the wavelength → all colors scatter equally (Mie scattering) → white
Danger signals are red: Red light scatters least → travels the farthest through fog/dust → best visibility at long range
Quick recall
Why does the Sun appear reddish at sunrise and sunset but white/yellowish at noon?
At noon, sunlight passes through a relatively thin layer of atmosphere — some blue scatters, making the sky blue, but enough of all colors reach your eye → white/yellowish Sun. At sunrise/sunset, light travels through much thicker atmosphere (longer path). Most blue and green wavelengths are scattered away over this long path. Only red/orange wavelengths survive → reddish Sun.
Tyndall Effect
The Tyndall effect is scattering of light by colloidal particles (larger than molecules but smaller than what you can see). It makes light beams visible in dusty/smoky rooms and is used to distinguish colloids from true solutions.
The Tyndall effect is the scattering of light by particles in a colloid or fine suspension. The particles (1-1000 nm) are larger than individual molecules but too small to see directly. When a beam of light passes through such a medium, it becomes visible as a bright cone or path.
Observed in colloids (milk, fog, smoke) but NOT in true solutions (salt water, sugar water)
Used as a test to distinguish colloids from true solutions — shine a laser: visible path = colloid, no visible path = true solution
The scattered light may be bluish if particles are small (Rayleigh-like) or white if particles are larger (Mie scattering)
The colour of scattered light depends on the size of the scattering particles relative to the wavelength of light
Blue colour of cigarette smoke: tiny particles → preferential blue scattering. White colour of exhaled smoke: larger particles (with moisture) → all colours scatter equally
Particles << wavelength (molecules)
Particles ~ wavelength (colloidal)
I 1/ ^4
Wavelength dependence varies with particle size
Examples: blue sky, red sunset
Examples: dusty room, fog, milk
Occurs in gases (atmosphere)
Occurs in colloids and suspensions
Always gives blue-dominant scattering
Can give blue, white, or reddish depending on particle size