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Na-update Mar 18, 2026

•

10 mga pahina

Understanding Lenses: Convex and Concave Explained

Lenses are everywhere - in your phone camera, glasses, and... Ipakita pa

1 / 10

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Introduction to Lenses

Ever wondered how your camera focuses or how glasses help you see clearly? It's all about refraction - the bending of light as it passes through different materials.

Converging (convex) lenses are thicker in the middle and bring light rays together at a focal point. Think of a magnifying glass - that's a converging lens. Diverging (concave) lenses are thinner in the middle and spread light rays apart.

The optical centre (O) is the middle of the lens where light passes straight through. The focal point (F) is where parallel light rays meet (or appear to come from), and the focal length (f) is the distance from the centre to this point.

Quick Tip: Remember "thick middle = converging, thin middle = diverging" to never mix them up!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Ray Diagrams for Converging Lenses

Drawing ray diagrams is like creating a map for light! You only need two special rays to find where an image forms.

For converging lenses, follow these three rules: 1) A ray parallel to the axis bends through the focal point, 2) A ray through the optical centre goes straight, and 3) A ray through the focal point becomes parallel to the axis.

The image you get depends entirely on where you place the object. If it's beyond 2F, you get a real, inverted, smaller image. Between F and 2F? Real, inverted, but magnified. Place it inside the focal length and boom - you've got a magnifying glass with a virtual, upright, enlarged image!

Exam Success: Learn the object position table by heart - it's a guaranteed marks winner!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Object Position and Image Types

Here's where converging lenses get interesting - the image changes dramatically based on object placement!

When your object sits beyond 2F, you get a real, inverted, diminished image between F and 2F. This is exactly how camera lenses work. At exactly 2F, the image appears at 2F on the other side, same size but upside down.

Place the object between F and 2F, and suddenly your image jumps beyond 2F, becoming real, inverted, but magnified. Put it right at F and no image forms - the rays become parallel. The magic happens inside F where you get a virtual, upright, magnified image.

Memory Trick: "Real images flip, virtual images don't" - real images are always inverted, virtual ones stay upright!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Diverging Lenses and Their Properties

Diverging lenses are the reliable ones - they always produce the same type of image, no matter where you put the object!

The ray rules are similar but with a twist: parallel rays appear to come from the focal point on the same side as the object. A ray towards the far focal point gets bent parallel to the axis.

No matter what you do with a diverging lens, you'll always get a virtual, upright, diminished image. Always. This makes them perfect for things like peepholes in doors or certain types of glasses for short-sightedness.

Study Smart: Since diverging lenses are predictable, focus your revision time on the trickier converging lens scenarios!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Lens Formula and Magnification Calculations

Time to put numbers to your diagrams! The lens formula connects everything: 1/f = 1/u + 1/v, where f is focal length, u is object distance, and v is image distance.

Magnification tells you how much bigger or smaller your image is: m = v/u. If m > 1, your image is magnified. If m < 1, it's diminished. Simple!

The sign convention is crucial: "Real is Positive" means real objects and images get positive distances, virtual images get negative distances. Converging lenses have positive focal lengths, diverging ones negative.

Calculation Confidence: Practice the sign convention until it's automatic - getting signs wrong will mess up your entire answer!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Worked Example: Ray Diagram Method

Let's solve a real problem! An object (2 cm tall) sits 6 cm from a converging lens with focal length 4 cm.

First, choose your scale - say 1 cm on paper = 2 cm reality. Draw your axis, mark the optical centre O, then place focal points F at 2 cm from O on your diagram.

Place your object 3 cm from O (representing 6 cm) and draw it 1 cm tall. Now trace your two main rays: one parallel to the axis (bends through F), another straight through O. Where they cross is your image!

Measuring gives us an image 6 cm from O on the diagram (12 cm in reality), 2 cm tall on diagram (4 cm reality). It's real, inverted, and magnified.

Diagram Success: Always use a ruler and draw large, clear diagrams - messy drawings lead to wrong answers!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Worked Example: Mathematical Method

Now let's use pure maths! Object at 10 cm from a converging lens with focal length 15 cm.

Using 1/f = 1/u + 1/v: 1/15 = 1/10 + 1/v. Rearranging: 1/v = 1/15 - 1/10 = 2/30 - 3/30 = -1/30. Therefore v = -30 cm.

The negative v means a virtual image! Magnification m = v/u = 30/10 = 3, so it's magnified threefold.

Since the object is inside the focal length (10 < 15), this makes perfect sense - the lens acts as a magnifying glass, creating a virtual, upright, magnified image 30 cm from the lens.

Check Your Logic: Always verify your mathematical answer makes physical sense - it prevents silly mistakes!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Sign Convention Deep Dive

Getting signs right separates the top students from the rest! The golden rule is "Real is Positive".

Object distance u is always positive (real objects). Focal length f is positive for converging lenses, negative for diverging ones. Image distance v is positive for real images, negative for virtual images.

When calculating magnification, use m = v/u with the actual values (including signs). The sign of v tells you if the image is real (positive) or virtual (negative).

A negative image distance always means virtual, upright image. A positive image distance means real, inverted image. Master this and you'll never get confused again!

Sign Mastery: Write "Real = +" at the top of every lens problem - it's your safety net!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Key Exam Points and Summary

Here's what you absolutely must remember for exams: lenses work by refraction, converging lenses have positive focal lengths and can form various image types, while diverging lenses have negative focal lengths and always form virtual, upright, diminished images.

For ray diagrams, know your three rules inside out. For calculations, master the lens formula $1/f = 1/u + 1/v$ and magnification $m = v/u$ .

The sign convention is your best friend - real is positive, virtual images have negative distances. A real image can be projected on a screen and is always inverted. A virtual image cannot be projected and is always upright.

Exam Strategy: Practice both ray diagrams and calculations for the same scenario - understanding both methods deeply will boost your confidence massively!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

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4.6/5

App Store

4.7/5

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Napakadaling gamitin at maganda ang disenyo ng app. Nahanap ko lahat ng hinahanap ko hanggang ngayon at natuto ako ng marami mula sa mga presentasyon! Tiyak na gagamitin ko ang app para sa isang takdang-aralin sa klase! At siyempre, nakakatulong din ito bilang inspirasyon.

Stefan S

gumagamit ng iOS

Sobrang ganda talaga ng app na ito. Maraming mga study notes at tulong [...]. Ang problemang subject ko ay Pranses, halimbawa, at ang app ay may maraming options para tumulong. Salamat sa app na ito, bumuti ang Pranses ko. Irerekumenda ko ito sa lahat.

Samantha Klich

Android user

Wow, talagang namangha ako. Sinubukan ko lang ang app dahil nakita ko itong ina-advertise nang maraming beses at sobrang nagulat ako. Ang app na ito ang TULONG na gusto mo para sa paaralan at higit sa lahat, nag-aalok ito ng maraming bagay, tulad ng workouts at fact sheets, na SOBRANG nakatulong sa akin.

Anna

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Pinakamagandang app sa mundo! walang masabi dahil sobrang ganda nito

Thomas R

iOS user

Napakaganda talaga. Nakakapag-review ako ng 10x mas mabuti, itong app ay mabilis na 10/10. Lubos kong inirerekomenda ito sa lahat. Pwede akong manood at maghanap ng notes. Pwede kong i-save ang mga ito sa subject folder. Pwede kong i-review anumang oras kapag bumalik ako. Kung hindi mo pa nasubukan ang app na ito, marami kang nawawala.

Basil

Android user

Ang app na ito ay nagpapalakas ng loob ko sa paghahanda sa exams, hindi lang dahil sa pagpapataas ng aking kumpiyansa sa sarili sa pamamagitan ng mga feature na nagpapahintulot sa iyo na makipag-connect sa iba at mabawasan ang pakiramdam na nag-iisa, kundi pati na rin sa paraan na nakatuon ang app sa pagpapagaan ng iyong pakiramdam. Madali itong i-navigate, masaya gamitin, at nakakatulong sa sinumang nahihirapan sa kahit anong paraan.

David K

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Sobrang galing ng app! Ilalagay ko lang ang paksa sa search bar at makakakuha na ako ng sagot kaagad. Hindi ko kailangang manood ng 10 YouTube videos para maintindihan ang isang bagay, kaya nakakatipid ako ng oras. Lubos na inirerekomenda!

Sudenaz Ocak

Android user

Sa paaralan, napakahina ko sa math pero salamat sa app, mas mahusay na ako ngayon. Lubos akong nagpapasalamat na ginawa niyo ang app na ito.

Greenlight Bonnie

Android user

napakareliable na app para tumulong at palawakin ang iyong mga ideya sa Math, English at iba pang mga related na paksa sa iyong mga gawain. gamitin mo ang app na ito kung nahihirapan ka sa mga area, susi ito para diyan. sana nag-review na ako dati. at libre rin ito kaya huwag mag-alala tungkol diyan.

Rohan U

Android user

Alam kong maraming apps gumagamit ng fake accounts para mapataas ang kanilang reviews pero ang app na ito ay deserve lahat ng papuri. Dati nakakakuha ako ng 4 sa aking English exams at ngayon nakakuha ako ng grade 7. Hindi ko pa alam ang app na ito tatlong araw bago ang exam at nakatulong ito ng SOBRA. Pakisuyong maniwala sa akin at gamitin ito dahil sigurado akong makikita mo rin ang mga pagbabago.

Xander S

iOS user

ANG MGA quiz AT flashcard SOBRANG HELPFUL AT I LOVE TALAGA SI Knowunity AI. PARANG CHATGPT LANG PERO MAS MATALINO!! NAKATULONG DIN SA MGA MASCARA PROBLEMS KO!! PATI NA RIN SA MGA TUNAY KONG subject! SYEMPRE 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

Grabe talaga ang app na to. Sobrang nakakaboring sakin ang pagreview pero ginagawa ng app na to na sobrang dali mag-organize ng lahat at pwede mong tanungin ang libreng ai para subukin ang sarili mo kaya sobrang buti at madali mong ma-upload ang sarili mong mga bagay. highly recommend bilang isang taong nagte-take ng mocks ngayon

Paul T

iOS user

Stefan S

gumagamit ng iOS

Samantha Klich

Android user

Anna

iOS user

Pinakamagandang app sa mundo! walang masabi dahil sobrang ganda nito

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

Sa paaralan, napakahina ko sa math pero salamat sa app, mas mahusay na ako ngayon. Lubos akong nagpapasalamat na ginawa niyo ang app na ito.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Physics

•

Na-update Mar 18, 2026

•

10 mga pahina

Understanding Lenses: Convex and Concave Explained

Lenses are everywhere - in your phone camera, glasses, and even your eyes! They're simply curved pieces of glass or plastic that bend light to create images. Understanding how they work is all about tracking light rays and knowing a... Ipakita pa

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Introduction to Lenses

Ever wondered how your camera focuses or how glasses help you see clearly? It's all about refraction - the bending of light as it passes through different materials.

Quick Tip: Remember "thick middle = converging, thin middle = diverging" to never mix them up!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Ray Diagrams for Converging Lenses

Drawing ray diagrams is like creating a map for light! You only need two special rays to find where an image forms.

Exam Success: Learn the object position table by heart - it's a guaranteed marks winner!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Object Position and Image Types

Here's where converging lenses get interesting - the image changes dramatically based on object placement!

Memory Trick: "Real images flip, virtual images don't" - real images are always inverted, virtual ones stay upright!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Diverging Lenses and Their Properties

Diverging lenses are the reliable ones - they always produce the same type of image, no matter where you put the object!

The ray rules are similar but with a twist: parallel rays appear to come from the focal point on the same side as the object. A ray towards the far focal point gets bent parallel to the axis.

Study Smart: Since diverging lenses are predictable, focus your revision time on the trickier converging lens scenarios!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Lens Formula and Magnification Calculations

Time to put numbers to your diagrams! The lens formula connects everything: 1/f = 1/u + 1/v, where f is focal length, u is object distance, and v is image distance.

Magnification tells you how much bigger or smaller your image is: m = v/u. If m > 1, your image is magnified. If m < 1, it's diminished. Simple!

Calculation Confidence: Practice the sign convention until it's automatic - getting signs wrong will mess up your entire answer!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Worked Example: Ray Diagram Method

Let's solve a real problem! An object (2 cm tall) sits 6 cm from a converging lens with focal length 4 cm.

First, choose your scale - say 1 cm on paper = 2 cm reality. Draw your axis, mark the optical centre O, then place focal points F at 2 cm from O on your diagram.

Measuring gives us an image 6 cm from O on the diagram (12 cm in reality), 2 cm tall on diagram (4 cm reality). It's real, inverted, and magnified.

Diagram Success: Always use a ruler and draw large, clear diagrams - messy drawings lead to wrong answers!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Worked Example: Mathematical Method

Now let's use pure maths! Object at 10 cm from a converging lens with focal length 15 cm.

Using 1/f = 1/u + 1/v: 1/15 = 1/10 + 1/v. Rearranging: 1/v = 1/15 - 1/10 = 2/30 - 3/30 = -1/30. Therefore v = -30 cm.

The negative v means a virtual image! Magnification m = v/u = 30/10 = 3, so it's magnified threefold.

Since the object is inside the focal length (10 < 15), this makes perfect sense - the lens acts as a magnifying glass, creating a virtual, upright, magnified image 30 cm from the lens.

Check Your Logic: Always verify your mathematical answer makes physical sense - it prevents silly mistakes!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Sign Convention Deep Dive

Getting signs right separates the top students from the rest! The golden rule is "Real is Positive".

When calculating magnification, use m = v/u with the actual values (including signs). The sign of v tells you if the image is real (positive) or virtual (negative).

A negative image distance always means virtual, upright image. A positive image distance means real, inverted image. Master this and you'll never get confused again!

Sign Mastery: Write "Real = +" at the top of every lens problem - it's your safety net!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Key Exam Points and Summary

For ray diagrams, know your three rules inside out. For calculations, master the lens formula $1/f = 1/u + 1/v$ and magnification $m = v/u$ .

Exam Strategy: Practice both ray diagrams and calculations for the same scenario - understanding both methods deeply will boost your confidence massively!

$# Lenses Introduction to lenses Lenses are curved pieces of transparent material (like glass or plastic) that refract light. Refraction is$

Mag-sign up para makita ang contentLibre ito!

Access sa lahat ng dokumento

Pagbutihin ang iyong mga grado

Sumali sa milyong mga estudyante

Akala namin hindi mo na itatanong...

Ano ang Knowunity AI companion?

Saan ko mada-download ang Knowunity app?

Maaari mong i-download ang app mula sa Google Play Store at Apple App Store.

Talaga bang libre ang Knowunity?

Tama 'yan! Mag-enjoy sa libreng access sa mga study content, makipag-connect sa kapwa mga estudyante, at kumuha ng instant na tulong – lahat nasa iyong daliri lang.

Smart Tools NEW

I-transform ang note na ito sa: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines

Praktis Exam

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Flashcards

Essay

Pinaka-sikat na nilalaman sa Physics

Speed, Distance, and Time

Students will learn the basic concepts of speed, distance, and time, and how they relate to each other in describing motion.

Physics

2nd Year

Balanced and Unbalanced Forces

Students will explore how balanced forces result in no change in motion, while unbalanced forces cause an object to accelerate or change direction.

Physics

2nd Year

Types of Forces

Students will identify common forces such as gravity (pulling objects down), friction (opposing motion), and air resistance (slowing objects in the air).

Physics

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Science/Physics notes - Speed, density, work

Speed density work formulas

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Understanding conduction, convection, and radiation with everyday examples of how heat moves through different materials and spaces.

Physics

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Learning the laws of reflection and applying them to plane mirrors to understand image formation (real vs. virtual, upright vs. inverted).

Physics

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Questions and answers for the leaving cert oral

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Outline of oral questions

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Students will learn about different types of data (qualitative, quantitative, discrete, continuous) and various methods for collecting primary and secondary data, including simple sampling.

Mathematics

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Hindi mo mahanap ang hinahanap mo? Tuklasin ang iba pang mga asignatura.

Gustong-gusto kami ng mga estudyante — at magiging ganoon ka rin.

4.6/5

App Store

4.7/5

Google Play

Stefan S

gumagamit ng iOS

Samantha Klich

Android user

Anna

iOS user

Pinakamagandang app sa mundo! walang masabi dahil sobrang ganda nito

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

Sa paaralan, napakahina ko sa math pero salamat sa app, mas mahusay na ako ngayon. Lubos akong nagpapasalamat na ginawa niyo ang app na ito.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user

Stefan S

gumagamit ng iOS

Samantha Klich

Android user

Anna

iOS user

Pinakamagandang app sa mundo! walang masabi dahil sobrang ganda nito

Thomas R

iOS user

Basil

Android user

David K

iOS user

Sudenaz Ocak

Android user

Sa paaralan, napakahina ko sa math pero salamat sa app, mas mahusay na ako ngayon. Lubos akong nagpapasalamat na ginawa niyo ang app na ito.

Greenlight Bonnie

Android user

Rohan U

Android user

Xander S

iOS user

Elisha

iOS user

Paul T

iOS user