Optical instruments — human eye, simple microscope, compound microscope, telescope: Question bank

2.5.8 · D5 · Physics › Optics › Optical instruments — human eye, simple microscope, compound

Definition Is page par har symbol, seedhe shabdon mein

Kisi bhi trap ko chhune se pehle, har letter ka exact matlab jaano (saari lengths cm mein).

$θ$ — visual angle: object se aane wali rays ka bundle jo tumhari aankhon par jo angle banata hai. Bada $θ$ = retina par badi picture.
$D$ — near point distance, normal aankhon ke liye $25 cm$ : normal aankh jitnee paas focus kar sakti hai.
$f$ — lens ki focal length ( $f_{o}$ objective, $f_{e}$ eyepiece). Chhota $f$ = zyada modhna (strongly bending).
$M$ — angular magnification: $M = θ_{with instrument} / θ_{naked eye}$ . $M_{D}$ iska woh value hai jab image near point par ho; $M_{\infty}$ jab image infinity par ho (relaxed eye).
$m_{o} = v_{o} / u_{o}$ — objective ki linear magnification (image height ÷ object height).
$u_{o}, v_{o}$ — objective ke liye object aur image distances. Sign convention (Lens equation and sign conventions): distances lens se measure hoti hain, outgoing-light direction mein positive. Real object ke liye $u_{o} < 0$ ; far side par real image ke liye $v_{o} > 0$ , isliye $m_{o} = v_{o} / u_{o}$ negative aata hai — minus sign inverted image hai, aur hum iska magnitude quote karte hain.
$L$ — tube length: objective–eyepiece separation, $\approx$ unke do foci ke beech ki distance.
$h$ — ek height (object ya intermediate image ki), $α, β$ — objective aur eyepiece par angles.

Formula

$M_{D} = 1 + D / f$ aur $M_{\infty} = D / f$ actually kahan se aate hain Ye dono poore page par milte hain, isliye inhe ek baar derive karte hain. Focal length $f$ ka ek magnifier object ko distance $u$ par rakhta hai (toh uska angle $θ = h / u$ hai) aur ek virtual image distance $v$ par dalta hai jahan aankh focus kar sake. Naked-eye reference angle $θ_{0} = h / D$ hai, isliye $M = θ / θ_{0} = D / u$ .

Relaxed eye: image ko infinity par bhejna ho toh object ko focus par rakho, $u = f$ . Tab $M_{\infty} = \frac{D}{f} .$
Image at near point: virtual image ko $v = - D$ tak force karo. Lens equation $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ deta hai $\frac{1}{u} = - \frac{1}{D} - \frac{1}{f}$ , isliye $M_{D} = \frac{D}{u} = 1 + \frac{D}{f} .$ "+1" kyun? Image $D$ par baith jaati hai infinity ki jagah, jisse object thoda sa $f$ ke paas aa jaata hai; woh extra closeness exactly ek unit $D / u$ hai — ek genuine geometric bonus jiske liye tum eye strain se pay karte ho. Neeche wali figure mein dono ray geometries side by side dikhti hain.

Figure — Optical instruments — human eye, simple microscope, compound microscope, telescope

True or false — justify

Magnifying glass ek object ko isliye bada dikhata hai kyunki woh object ki real size badhata hai.

False — physically kuch bhi size nahi badlta; lens woh angle

θ

badhata hai jo object tumhari aankh par subtend karta hai, aur retinal image size usi angle ke saath hoti hai (dekho Linear vs angular magnification).

Angular magnification

M = 1

matlab instrument bekaar hai.

True zyada karne ke sense mein —

M = 1

matlab near point par naked eye jaisi hi visual angle, toh retinal image badi nahi hoti.

Simple microscope ke liye, image near point par dekhna hamesha relaxed eye se dekhne se zyada magnification deta hai.

True —

M_{D} = 1 + D / f

M_{\infty} = D / f

se exactly

1

zyada hota hai, lekin "+1" ke liye eye strain ki cost lagti hai, isliye relaxed viewing magnification ko comfort se trade karta hai.

Ek telescope kisi tare ki ek magnified real image banata hai jo tum eyepiece par screen par pakad sako.

False — normal adjustment mein final rays eyepiece se parallel nikalti hain (image at infinity); ek telescope angle magnify karta hai, linear size nahi, isliye pakadne ke liye koi finite screen image hoti hi nahi.

Objective focal length badhane se microscope aur telescope dono ki magnification badhti hai.

False — telescope

M = f_{o} / f_{e}

lambe

f_{o}

se badhti hai, lekin microscope objective ko chhota

f_{o}

chahiye kyunki

m_{o} \approx L / f_{o}

f_{o}

chhotey hone par badhta hai.

Compound microscope ki total magnification dono lenses ki powers ka sum hai.

False — eyepiece pehle se magnify ho chuki intermediate image ko magnify karta hai, isliye effects multiply hote hain:

M = m_{o} m_{e}

, bilkul series mein do photocopiers ki tarah.

Bada telescope objective hamesha zyada magnification deta hai.

False — zyada wide objective light-gathering aur resolving power improve karta hai, lekin magnification sirf focal length ratio

f_{o} / f_{e}

par depend karti hai, aperture diameter par nahi.

Magnifying glass ke liye, object ko lens ke paas laane se magnification bina kisi limit ke badhti rehti hai.

False — object focal length ke andar rehna chahiye;

M_{D} = 1 + D / f

f

aur

D

se fix hota hai, object ko thoda hilane se nahi, isliye ek hard ceiling hai.

Zyada magnification ka matlab hamesha yeh hai ki tum object ka zyada hissa ek saath dekhoge.

False — magnification aur field of view trade off karte hain:

M

badhane par eyepiece jo angles accept karta hai ka cone narrow ho jaata hai, isliye tum ek chhota patch dekhte ho, sirf bada hua.

Spot the error

"Ek student telescope ki power

M = D / f_{o} = 25/100

compute karta hai."

Near-point distance

D

ka yahan koi kaam nahi — object infinity par hai, isliye reference angle tare ka real angle

α = h / f_{o}

hai, jo deta hai

M = f_{o} / f_{e}

, na ki

D / f

"Telescope ka

M = f_{o} / f_{e}

sirf assert kiya gaya hai; iske peeche koi reason nahi."

Rays trace karo: angle

α

par parallel light objective ke focal plane mein height

h

ke ek spot par focus hoti hai, isliye small angles se (neeche figure dekho)

α = h / f_{o}

. Wahi height eyepiece focus par baithi hai, angle

β = h / f_{e}

par parallel rays banke nikalti hai. Divide karo:

M = β / α = (h / f_{e}) / (h / f_{o}) = f_{o} / f_{e}

"Ek cell ko

\times 300

magnify karne ke liye hum sirf itna chhota

f

wala ek lens chunte hain ki

1 + D / f = 300

ho jaaye."

Ek akela lens itni power nahi pahunch sakta bina absurdly chhote

f

aur severe aberrations ke; yahi wajah hai ki compound microscope kaam ko ek objective aur eyepiece mein baant deta hai jo multiply karte hain.

"Compound microscope mein intermediate image virtual aur erect hoti hai."

Galat — objective ek real, inverted, enlarged image banata hai eyepiece ke focus ke thoda andar; eyepiece phir us real image ko apna object maanke treat karta hai.

"Normal setting mein compound microscope ki tube length

f_{o} + f_{e}

hai."

Woh telescope formula hai. Microscope ke liye

L \approx v_{o} + f_{e}

(roughly do foci ka separation); object

f_{o}

ke thoda sa bahar baithta hai, agar wahan nahi.

"Telescope mein eyepiece ki focal length lambi honi chahiye taaki zyada dikhey."

Ulta hai —

M = f_{o} / f_{e}

tab badhti hai jab

f_{e}

chhota ho; lamba eyepiece focal length magnification ko ghata deta hai.

"Ek insaan ka near point

25 cm

hai, isliye har instrument formula

D = 25 cm

use karta hai."

Sirf normal aankh ke liye — hypermetropic aankh ka near point bada hota hai, jo

D

change karta hai (dekho Defects of vision — myopia, hypermetropia); aur telescope formulas

D

ko bilkul ignore karte hain.

"Kyunki

m_{o} = v_{o} / u_{o}

hai,

u_{o}

ko huge banane se objective magnification boost hogi."

Bada

u_{o}

matlab object door hai, isliye real image barely magnify hoti hai; objective tab sabse zyada magnify karta hai jab object

f_{o}

ke thoda bahar ho (chhota

∣ u_{o} ∣ \approx f_{o}

), jo deta hai

m_{o} \approx L / f_{o}

. Yaad raho

u_{o} < 0

real object ke liye, isliye "huge

u_{o}

" matlab door, paas nahi.

"Sirf magnification enormous karo aur tum koi bhi tiny detail resolve kar loge."

Empty magnification — objective ke numerical aperture se set hone wali limit ke baad, tum blur enlarge karte ho, detail nahi; microscope ke liye useful

M

approximately

1000 \times

numerical aperture tak cap hota hai, jiske baad diffraction-limited resolution (Resolving power and diffraction limit) improve karne se manaa kar deti hai.

Why questions

Kisi instrument ki magnification angles ke ratio ko use kyun karta hai, na ki image heights ke ratio ko?

Kyunki tumhari retina par picture ki size uss angle se set hoti hai jo rays ka bundle aankh par banata hai, isliye do bahut alag size ke objects "barabar" lagte hain agar unke visual angles match karein.

Simple microscope ki relaxed-eye power near-point power se exactly

1

kyun kam hoti hai?

M_{D} - M_{\infty} = (1 + D / f) - (D / f) = 1

; "+1" woh extra angle hai jo tum virtual image ko infinity se near point

D

tak kheenchne ki strain se paate ho.

Magnifying lens ke liye hum chhota focal length kyun chahte hain lekin telescope objective ke liye lamba wala?

Chhota

f

ek paas ke object ko bahut karib rakhne deta hai (huge

D / f

angle boost); telescope ka object infinity par hai, aur lamba

f_{o}

uski focal-plane image badi banata hai taaki eyepiece angle

h / f_{e}

bada ho. ::: Sankshep mein:

D / f

f_{o} / f_{e}

focal lengths ko ulti dishan mein kheenchte hain.

Tum near point se paas koi object focus kyun nahi kar sakte chahe woh bada angle subtend kare?

Tumhari eye lens apni focal length sirf itni hi ghata sakti hai (accommodation ki limit hoti hai); near point se paas image retina ke peeche land karti hai aur blur ho jaati hai, isliye ek bada angle jo tum sharpen nahi kar sakte woh bekaar hai.

Compound microscope image ko invert kyun karta hai jabki magnifying glass erect rakhta hai?

Magnifying glass ek virtual, erect image banata hai (object

f

ke andar); compound objective ek real, inverted image banata hai, aur eyepiece bina re-invert kiye re-magnify karta hai, isliye final view inverted hota hai.

Objective aperture bada karna kyun help karta hai chahe

M

nahi badlta?

Zyada wide aperture zyada light collect karta hai aur diffraction limit ko ghata deta hai, isliye tum zyada barik, zyada dim detail dekh sakte ho — resolution improve hoti hai, magnification nahi.

Tumhari aankh ki pupil ka size telescopic image ki brightness ko kyun cap karta hai?

Eyepiece se exit beam pupil (

\approx 2

–

7 mm

) mein fit honi chahiye; agar exit pupil zyada wide hai, baaki waste hota hai, isliye ek telescope cheezein per unit area mein ek achhi tarah lit naked-eye view se zyada bright nahi bana sakta — woh sirf light ko zyada bade angle par spread karta hai.

Ek reflecting telescope ek aise problem se kyun bachta hai jo lambe refractor ko satata hai?

Ek curved mirror sabhi colours ko same focus par reflect karta hai (chromatic aberration nahi) aur koi huge, sagging glass lens nahi chahiye, isliye large-aperture telescopes almost hamesha reflectors hote hain.

Edge cases

Simple microscope ki magnification kya hogi jab object exactly focus par rakha jaaye?

Virtual image infinity par jaati hai (relaxed eye), jo deta hai

M = D / f

— yeh usable magnification ka minimum hai, maximum nahi.

Kya hoga magnifying power ka jab fixed

D

ke liye

f \to 0

M = 1 + D / f \to \infty

mathematically, lekin practically tiny

f

matlab severe aberrations aur impossibly close object, isliye ideal formula bahut pehle hi break down ho jaata hai.

Koi instrument kya magnification deta hai jab object exactly near point par bina lens ke rakha jaaye?

Definition se

M = 1

— yahi reference case

θ_{0} = h / D

hai jisse har magnifying power divide hoti hai, isliye "no instrument" unity deta hai.

Kisi nearby object (infinity par nahi) ko dekhte waqt telescope ke liye kya

M = f_{o} / f_{e}

exactly hold karta hai?

Nahi — derivation assume karti hai parallel incoming rays (

α = h / f_{o}

); finite-distance object ke liye objective image exactly apne focal plane mein nahi baith-ti, isliye simple ratio sirf approximate hai.

Ek real telescope se tare ki "angular size" kya hoti hai, aur woh exactly zero kyun nahi hoti?

Ek tara ek point hai, lekin diffraction use finite angular radius

\approx 1.22 λ / D_{aperture}

ke ek Airy disk mein spread karta hai (Resolving power and diffraction limit); magnify karna sirf is blur disk ko enlarge karta hai, yahi wajah hai ki raw magnification kabhi tare ko sharpen nahi karta.

Kya neat formulas poore field of view mein hold karte hain, ya sirf axis ke paas?

Sirf axis ke paas (paraxial) — off-axis mein tum field curvature (sharp image ek curved surface par hoti hai, isliye jab centre focused ho toh edges blur ho jaate hain) aur aberrations (coma, astigmatism) se milte ho jo koi single ideal number capture nahi karta.

Zyada magnification chase karna image ko better ki jagah worse kab bana deta hai?

Jab tum diffraction/aberration limit se aage nikal jaao: extra

M

blur ko magnify karta hai aur field dim kar deta hai (light zyada area par spread hoti hai), isliye ek optimum

M

hota hai jiske baad detail aur brightness dono degrade hoti hain.

Recall Jane se pehle one-line self-test

Har ek dhako aur reason ke saath jawab do: Microscope ko chhota $f$ chahiye, telescope ko lamba $f_{o}$ — split kyun? ::: Near object ko close placement chahiye ( $D / f$ ); infinite object ko badi focal-plane image chahiye ( $f_{o} / f_{e}$ ). Compound microscope ke liye multiply kyun, add kyun nahi? ::: Eyepiece objective ke output ko magnify karta hai, isliye gains compound hote hain. Telescope formula mein $D$ kyun nahi hota? ::: Uska object infinity par hai, isliye reference angle real angle $α = h / f_{o}$ hai, $h / D$ nahi. $M_{D} = 1 + D / f$ mein "+1" kahan se aata hai? ::: Virtual image ko infinity se near point $D$ tak kheenchne se object thoda paas aa jaata hai, jo $D / u$ ki ek extra unit ke barabar hai.