•

Aktualisiert Mar 18, 2026

•

10 Seiten

Understanding Lenses: Convex and Concave Explained

Lenses are everywhere - in your phone camera, glasses, and... Mehr anzeigen

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!

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

Wir dachten schon, du fragst nie...

Was ist der Knowunity KI-Begleiter?

Unser KI-Begleiter ist ein speziell für Schüler entwickeltes KI-Tool, das mehr als nur Antworten bietet. Basierend auf Millionen von Knowunity-Inhalten liefert er relevante Informationen, personalisierte Lernpläne, Quizze und Inhalte direkt im Chat und passt sich deinem individuellen Lernweg an.

Wo kann ich die Knowunity-App herunterladen?

Du kannst die App im Google Play Store und im Apple App Store herunterladen.

Ist Knowunity wirklich kostenlos?

Genau! Genieße kostenlosen Zugang zu Lerninhalten, vernetze dich mit anderen Schülern und hol dir sofortige Hilfe – alles direkt auf deinem Handy.

Beliebtester Inhalt in 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

2nd Year

Science/Physics notes - Speed, density, work

Speed density work formulas

Science

5th Year

Methods of Heat Transfer

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

Physics

3rd Year

Reflection of Light

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

Physics

5th Year

Beliebtester Inhalt

Irish oral questions and answers

Questions and answers for the leaving cert oral

Irish

5th Year

LC HL notes- Iníon (poem)

Includes poem in English and Irish, theme, key words & phrases

Irish

5th Year

Gaeilge Grammar Office

All the basics you need to know on Irish grammar.

Irish

6th Year

Elizabeth Bishop notes

English

6th Year

Irish oral questions

Outline of oral questions

Irish

5th Year

Cultural Context : Shawshank Redemption : Sive : Small Things Like These

Comparative Study : Cultural Context : Shawshank Redemption, Sive and Small Things Like These

English

6th Year

Elizabeth bishop notes

Everything you need to know about Elizabeth bishop.

English

5th Year

The outsiders

Movie we studied

English

3rd Year

Data Collection and Types of Data

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

2nd Year

Findest du nicht, was du suchst? Entdecke andere Fächer.

Schüler lieben uns — und du auch.

4.6/5

App Store

4.7/5

Google Play

Die App ist sehr einfach zu bedienen und gut gestaltet. Ich habe bisher alles gefunden, wonach ich gesucht habe, und konnte viel aus den Präsentationen lernen! Ich werde die App definitiv für ein Schulprojekt nutzen! Und natürlich hilft sie auch sehr als Inspiration.

Stefan S

iOS-Nutzer

Diese App ist wirklich super. Es gibt so viele Lernzettel und Hilfen [...]. Mein Problemfach ist zum Beispiel Französisch und die App hat so viele Möglichkeiten zur Hilfe. Dank dieser App habe ich mich in Französisch verbessert. Ich würde sie jedem empfehlen.

Samantha Klich

Android-Nutzerin

Wow, ich bin wirklich begeistert. Ich habe die App einfach mal ausprobiert, weil ich sie schon oft beworben gesehen habe und war absolut beeindruckt. Diese App ist DIE HILFE, die man für die Schule braucht und vor allem bietet sie so viele Dinge wie Übungen und Lernzettel, die mir persönlich SEHR geholfen haben.

Anna

iOS-Nutzerin

Beste App der Welt! Keine Worte, weil sie einfach zu gut ist

Thomas R

iOS-Nutzer

Einfach genial. Lässt mich 10x besser lernen, diese App ist eine glatte 10/10. Ich empfehle sie jedem. Ich kann Lernzettel anschauen und suchen. Ich kann sie im Fachordner speichern. Ich kann sie jederzeit wiederholen, wenn ich zurückkomme. Wenn du diese App noch nicht ausprobiert hast, verpasst du wirklich was.

Basil

Android-Nutzer

Diese App hat mich so viel selbstbewusster in meiner Klausurvorbereitung gemacht, nicht nur durch die Stärkung meines Selbstvertrauens durch die Features, die es dir ermöglichen, dich mit anderen zu vernetzen und dich weniger allein zu fühlen, sondern auch durch die Art, wie die App selbst darauf ausgerichtet ist, dass du dich besser fühlst. Sie ist einfach zu bedienen, macht Spaß und hilft jedem, der in irgendeiner Weise Schwierigkeiten hat.

David K

iOS-Nutzer

Die App ist einfach super! Ich muss nur das Thema in die Suche eingeben und bekomme sofort eine Antwort. Ich muss nicht mehr 10 YouTube-Videos schauen, um etwas zu verstehen, und spare dadurch richtig viel Zeit. Sehr empfehlenswert!

Sudenaz Ocak

Android-Nutzerin

In der Schule war ich echt schlecht in Mathe, aber dank der App bin ich jetzt besser geworden. Ich bin so dankbar, dass ihr die App gemacht habt.

Greenlight Bonnie

Android-Nutzerin

sehr zuverlässige App, um deine Ideen in Mathe, Englisch und anderen verwandten Themen zu verbessern. bitte nutze diese App, wenn du in bestimmten Bereichen Schwierigkeiten hast, diese App ist dafür der Schlüssel. wünschte, ich hätte früher eine Bewertung geschrieben. und sie ist auch kostenlos, also mach dir darüber keine Sorgen.

Rohan U

Android-Nutzer

Ich weiß, dass viele Apps gefälschte Accounts nutzen, um ihre Bewertungen zu pushen, aber diese App verdient das alles. Ursprünglich hatte ich eine 4 in meinen Englisch-Klausuren und dieses Mal habe ich eine 2 bekommen. Ich wusste erst drei Tage vor der Klausur von dieser App und sie hat mir SEHR geholfen. Bitte vertrau mir wirklich und nutze sie, denn ich bin sicher, dass auch du Fortschritte sehen wirst.

Xander S

iOS-Nutzer

DIE QUIZZE UND KARTEIKARTEN SIND SO NÜTZLICH UND ICH LIEBE Knowunity KI. ES IST AUCH BUCHSTÄBLICH WIE CHATGPT ABER SCHLAUER!! HAT MIR AUCH BEI MEINEN MASCARA-PROBLEMEN GEHOLFEN!! SOWIE BEI MEINEN ECHTEN FÄCHERN! NATÜRLICH 😍😁😲🤑💗✨🎀😮

Elisha

iOS-Nutzer

Diese App ist echt der Hammer. Ich finde Lernen so langweilig, aber diese App macht es so einfach, alles zu organisieren und dann kannst du die kostenlose KI bitten, dich abzufragen, so gut, und du kannst einfach deine eigenen Sachen hochladen. sehr empfehlenswert als jemand, der gerade Probeklausuren schreibt

Paul T

iOS-Nutzer

Stefan S

iOS-Nutzer

Samantha Klich

Android-Nutzerin

Anna

iOS-Nutzerin

Beste App der Welt! Keine Worte, weil sie einfach zu gut ist

Thomas R

iOS-Nutzer

Basil

Android-Nutzer

David K

iOS-Nutzer

Sudenaz Ocak

Android-Nutzerin

In der Schule war ich echt schlecht in Mathe, aber dank der App bin ich jetzt besser geworden. Ich bin so dankbar, dass ihr die App gemacht habt.

Greenlight Bonnie

Android-Nutzerin

Rohan U

Android-Nutzer

Xander S

iOS-Nutzer

Elisha

iOS-Nutzer

Paul T

iOS-Nutzer

Physics

•

Aktualisiert Mar 18, 2026

•

10 Seiten

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... Mehr anzeigen

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

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!

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

Melde dich an, um den Inhalt zu sehenKostenlos!

Zugriff auf alle Dokumente

Verbessere deine Noten

Schließ dich Millionen Schülern an

Wir dachten schon, du fragst nie...

Was ist der Knowunity KI-Begleiter?

Wo kann ich die Knowunity-App herunterladen?

Du kannst die App im Google Play Store und im Apple App Store herunterladen.

Ist Knowunity wirklich kostenlos?

Genau! Genieße kostenlosen Zugang zu Lerninhalten, vernetze dich mit anderen Schülern und hol dir sofortige Hilfe – alles direkt auf deinem Handy.

Smart Tools NEU

Verwandle diesen Lernzettel in: ✓ 50+ Übungsfragen ✓ Interaktive Karteikarten ✓ Komplette Probeklausur ✓ Aufsatzgliederungen

Probeklausur

Quiz

Karteikarten

Aufsatz

Beliebtester Inhalt in 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

2nd Year

Science/Physics notes - Speed, density, work

Speed density work formulas

Science

5th Year

Methods of Heat Transfer

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

Physics

3rd Year

Reflection of Light

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

Physics

5th Year

Beliebtester Inhalt

Irish oral questions and answers

Questions and answers for the leaving cert oral

Irish

5th Year

LC HL notes- Iníon (poem)

Includes poem in English and Irish, theme, key words & phrases

Irish

5th Year

Gaeilge Grammar Office

All the basics you need to know on Irish grammar.

Irish

6th Year

Elizabeth Bishop notes

English

6th Year

Irish oral questions

Outline of oral questions

Irish

5th Year

Cultural Context : Shawshank Redemption : Sive : Small Things Like These

Comparative Study : Cultural Context : Shawshank Redemption, Sive and Small Things Like These

English

6th Year

Elizabeth bishop notes

Everything you need to know about Elizabeth bishop.

English

5th Year

The outsiders

Movie we studied

English

3rd Year

Data Collection and Types of Data

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

2nd Year

Findest du nicht, was du suchst? Entdecke andere Fächer.

Schüler lieben uns — und du auch.

4.6/5

App Store

4.7/5

Google Play

Stefan S

iOS-Nutzer

Samantha Klich

Android-Nutzerin

Anna

iOS-Nutzerin

Beste App der Welt! Keine Worte, weil sie einfach zu gut ist

Thomas R

iOS-Nutzer

Basil

Android-Nutzer

David K

iOS-Nutzer

Sudenaz Ocak

Android-Nutzerin

In der Schule war ich echt schlecht in Mathe, aber dank der App bin ich jetzt besser geworden. Ich bin so dankbar, dass ihr die App gemacht habt.

Greenlight Bonnie

Android-Nutzerin

Rohan U

Android-Nutzer

Xander S

iOS-Nutzer

Elisha

iOS-Nutzer

Paul T

iOS-Nutzer

Stefan S

iOS-Nutzer

Samantha Klich

Android-Nutzerin

Anna

iOS-Nutzerin

Beste App der Welt! Keine Worte, weil sie einfach zu gut ist

Thomas R

iOS-Nutzer

Basil

Android-Nutzer

David K

iOS-Nutzer

Sudenaz Ocak

Android-Nutzerin

In der Schule war ich echt schlecht in Mathe, aber dank der App bin ich jetzt besser geworden. Ich bin so dankbar, dass ihr die App gemacht habt.

Greenlight Bonnie

Android-Nutzerin

Rohan U

Android-Nutzer

Xander S

iOS-Nutzer

Elisha

iOS-Nutzer

Paul T

iOS-Nutzer