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Which of the following statements is true for a convex lens?

It converges parallel rays of light.. Tests basic understanding of convex lens properties.

If an object is placed between the principal focus (F) and the optical center (O) of a convex lens, the image formed will be:

Virtual, erect, enlarged. Tests knowledge of image formation for a specific object position (magnifying glass case).

A convex lens has a focal length of 20 cm. An object is placed 30 cm from the lens. What is the nature of the image?

Real, inverted, enlarged. Requires applying the lens formula or knowing the image formation rules for object between F and 2F.

Physics · Class 9-10 · CBSE

Light and Convex Lenses

Aconvex lensis a converging lens, meaning it brings parallel rays of light together at a single point. Understanding how light interacts with these lenses is crucial for predicting image formation.

1How Convex Lenses Work

A convex lens is thicker in the middle and thinner at the edges. It causes parallel rays of light toconvergeat a point called the principal focus ( $F$ ). This converging property is why they are used in magnifying glasses and cameras.

Light Rays Through a Convex Lens: Principal Axis, Optical Center (O), Principal Focus (F), Parallel Rays, Converged Rays — Light Rays Through a Convex Lens
Parallel light rays converge at the principal focus after passing through a convex lens.
1Principal Axis — Imaginary line passing through the optical center
2Optical Center (O) — Central point of the lens
3Principal Focus (F) — Point where parallel rays converge
4Parallel Rays — Light rays entering the lens
5Converged Rays — Rays after passing through the lens

2Key Ray Tracing Rules

To predict where an image will form, we useray tracingwith specific rules. By drawing just two or three principal rays, we can locate the image's position, size, and nature.

Rules for Ray Tracing with Convex Lenses

Incident Ray	Refracted Ray
Parallel to principal axis	Passes through principal focus (F) on the other side
Passing through principal focus (F)	Becomes parallel to principal axis
Passing through optical center (O)	Goes undeviated

Parallel to principal axis
Refracted Ray
Passes through principal focus (F) on the other side
Passing through principal focus (F)
Refracted Ray
Becomes parallel to principal axis
Passing through optical center (O)
Refracted Ray
Goes undeviated

3Image Formation at Different Object Positions

Theposition of the objectrelative to the convex lens significantly changes the characteristics of the image formed. We define $F$ as the principal focus and $2F$ as twice the focal length.

Image Characteristics with Object Position

1
Object at Infinity
Image at F, real, inverted, highly diminished
2
Object beyond 2F
Image between F and 2F, real, inverted, diminished
3
Object at 2F
Image at 2F, real, inverted, same size
4
Object between F and 2F
Image beyond 2F, real, inverted, enlarged
5
Object at F
Image at infinity, real, inverted, highly enlarged
6
Object between F and O
Image on same side as object, virtual, erect, enlarged

Did you know? Did you know that the human eye's lens is a convex lens, focusing light onto the retina to form an inverted image, which our brain then flips right-side up?

4Lens Formula and Magnification

Thelens formularelates the object distance ( $u$ ), image distance ( $v$ ), and focal length ( $f$ ). Magnification ( $m$ ) describes how much larger or smaller the image is compared to the object.

Lens Formula

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

$u$ = object distance
$v$ = image distance
$f$ = focal length

Magnification Formula

m = \frac{h'}{h} = \frac{v}{u}

$m$ = magnification
$h'$ = height of image
$h$ = height of object

Common mistake: Remember to use the correct sign conventions for

u

v

, and

f

. For convex lenses,

f

is positive. Object distance (

u

) is always negative if placed to the left of the lens.

5Example: Object between F and 2F

Real-life example · Image Formation Example

An object is placed 15 cm from a convex lens with a focal length of 10 cm. Here, the object is between F (10 cm) and 2F (20 cm). Using the lens formula, we find the image distance $v = 30$ cm. The image is formed beyond 2F, is real, inverted, and enlarged ( $m = -2$ ). This setup is similar to a projector.

Exam tip: For exam questions, always draw a rough ray diagram first to visualize the image formation before applying formulas. This helps in checking your answer.

6Exam Corner

Important for exams

Convex lenses areconverging lenses.
Principal focus ( $F$ ) is where parallel rays converge.
Ray tracing rules help locate images.
Image characteristics (real/virtual, erect/inverted, size) depend onobject position.
Lens formula: $1/v - 1/u = 1/f$ .
Magnification: $m = h'/h = v/u$ .
Sign conventions are crucial for calculations.

Exam question · NEET 2019 style

An object is placed at a distance of 2F from a convex lens. The image formed will be:

A.Real, inverted, diminished
B.Real, inverted, same size
C.Virtual, erect, enlarged
D.Real, erect, enlarged

Remember it: RIVS: Real, Inverted, Virtual, Same side (for virtual images with convex lenses).

Remember

Convex lensesconvergelight rays.
Image characteristics depend on theobject's positionrelative to F and 2F.
Ray tracingand thelens formulaare used to predict image formation.
Real images areinverted, virtual images areerect.
Magnification indicates thesize of the imagerelative to the object.

Check yourself

Question 1
Which of the following statements is true for a convex lens?
Question 2
If an object is placed between the principal focus (F) and the optical center (O) of a convex lens, the image formed will be:
Question 3
A convex lens has a focal length of 20 cm. An object is placed 30 cm from the lens. What is the nature of the image?