What happens to parallel rays of light when they pass through a convex lens?

Parallel rays of light passing through a convex lens converge at the focal point, with the distance from the lens center to the focal point known as the focal length.

How does the image formed by a convex lens change as the object distance increases?

As the object distance increases from a convex lens, the image moves closer to the focal point. Initially, if the object is at a distance larger than twice the focal length, the image will be real, inverted, and smaller. As the object moves farther away, the image becomes more focused and diminishes in size.

Can a convex lens produce a virtual image?

Indeed, a convex lens can produce a virtual image, but this happens only when the object is positioned closer to the lens than its focal length. In this case, the virtual image will appear upright and magnified.

What separates a real image from a virtual image created by a convex lens?

A real image is formed when the refracted light rays converge at a point after passing through the convex lens. It is inverted and can be projected onto a screen. A virtual image, on the other hand, occurs when the light rays diverge, and the image appears to be formed on the same side of the lens as the object. It is upright and cannot be projected onto a screen.

How does the curvature of a convex lens affect its focal length?

The curvature of the convex lens affects its focal length. A lens with a greater curvature (a steeper shape) will have a shorter focal length, while a lens with a flatter curvature will have a longer focal length. The stronger the curvature, the more the light is refracted and the closer the focal point will be.

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Convex Lens

It is a transparent optical device that converges light rays passing through it to a single point called the focal point. It is thicker at the center than at the edges and is commonly used to form real or magnified images. Convex lenses are found in everyday objects like eyeglasses, magnifying glasses, and cameras. They come in different types, including plano-convex and double-convex lenses, and are essential in optical systems due to their ability to focus light.

1.0Definition of Convex Lens

A lens is a portion of a transparent material with two refracting surfaces such that at least one is curved with the refractive index of its material being different from that of the surroundings.
A thin spherical lens with refractive index greater than that of surroundings behaves as a convergent or convex lens, i.e., converges parallel rays if its central (i.e. paraxial) portion is thicker than marginal one.

2.0Types of Convex Lens

3.0Principal Focus of Convex Lens

Principal Focus: A Lens has two focal points.

First Focus: First focal point is an object point on the principal axis corresponding to which the image is formed at infinity.

Principal Focus of Convex Lens ( First Focus)

Second Focus: Second focal point is an image point on the principal axis corresponding to which object lies at infinity.

Second Focus (Principal Focus of Convex Lens)

4.0Rules For Image Formation In Convex Lens

A ray passing through the optical centre proceeds without deviation through the lens.
A ray passing through first focus or directed towards it, becomes parallel to the principal axis after refraction from the lens.
A ray passing parallel to the principal axis passes or appears to pass through F after refraction through the lens.

5.0Image Formation In Convex Lens

6.0Image formation in Convex Lens

Position of Object- Placed at Infinity
Position of Image-Formed at f
Nature-Real, Inverted
Size-Highly Diminished

Image formation in Convex Lens : Position of Object- Placed at Infinity Position of Image-Formed at f Nature-Real,Inverted Size-Highly Diminished

Position of Object- Placed at -∞ and 2f
Position of Image-Formed in between 2f and f
Nature-Real,Inverted
Size- Diminished

Image formation in Convex Lens: Position of Object- Placed at -∞ and 2f Position of Image-Formed in between 2f and f Nature-Real,Inverted Size- Diminished

Position of Object- Placed at -2f
Position of Image-Formed at 2f
Nature-Real,Inverted
Size- Equal in size

Image formation in Convex Lens: Position of Object- Placed at -2f Position of Image-Formed at 2f Nature-Real,Inverted Size- Equal in size

Position of Object- Placed in between -2f and -f
Position of Image-In between 2f and ∞
Nature-Real,Inverted
Size- Enlarged

Image formation in Convex Lens: Position of Object- Placed in between -2f and -f Position of Image-In between 2f and ∞ Nature-Real,Inverted Size- Enlarged

Position of Object- Placed in between -2f and -f ( very nearer to -f)
Position of Image-Formed At ∞
Nature-Real,Inverted
Size- Enlarged

Image formation in Convex Lens: Position of Object- Placed in between -2f and -f ( very nearer to -f) Position of Image-Formed At ∞ Nature-Real,Inverted Size- Enlarged

Position of Object- Object is Placed in between -f and optical centre ( very nearer to -f)
Position of Image-Formed At - ∞
Nature-Virtual,Erect
Size- Highly Enlarged

Image formation in Convex Lens: Position of Object- Object is Placed in between -f and optical centre ( very nearer to -f) Position of Image-Formed At - ∞ Nature-Virtual,Erect Size- Highly Enlarged

Position of Object- Object is Placed in between -f and optical centre
Position of Image-In between - ∞ and Optical Centre
Nature-Virtual,Erect
Size- Enlarged

Image formation in Convex Lens: Position of Object- Object is Placed in between -f and optical centre Position of Image-In between - ∞ and Optical Centre Nature-Virtual,Erect Size- Enlarged

7.0Lens Formula For Convex Lens

Object AB is positioned between the optical centre and and focus of the convex lens.Image A’B’ formed by convex lens is virtual,erect and magnified.

$Δ A^{'} B^{'} O and A BO are similar$

$\frac{A ^{'} B ^{'}}{A B} = \frac{B ^{'} O}{B ^{'} O}$ ……….(1)

$Δ A^{'} B^{'} F and MOF$ are similar

$\frac{A ^{'} B ^{'}}{MO} = \frac{BF}{OF}$

MO=AB therefore

$\frac{A ^{'} B ^{'}}{A B} = \frac{BF}{OF}$ ……….(2)

$\frac{- v}{- u} = \frac{- f + v}{- f}$

$v f = u f - uv \Rightarrow uv = u f - v f$

Dividing both sides by uvf we get

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

8.0Magnification for Convex Lens

It is defined as the ratio of the size of image formed by the lens to the size of the object.

$m = \frac{Size of Image}{Size of Object} = \frac{h _{2}}{h _{1}} = \frac{v}{u}$

Linear Magnification in terms of u and f

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

Multiplying both sides by u

$\frac{u}{v} - 1 = \frac{u}{f} \Rightarrow \frac{u}{v} = \frac{f + u}{f}$

$m = \frac{1}{u} = \frac{f}{f + u}$

Linear Magnification in terms of v and f

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

Multiplying both sides by v

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

$m = \frac{v}{u} = \frac{f - v}{f}$

Example-1.An object and a screen are positioned 90 cm apart. What is the required focal length and type of lens needed to form a distinct image on the screen, two times the the size of the object?

Solution:Since the image is real, a convex lens should be placed between the object and the screen.

u=-x

v=90-x

$m = \frac{v}{u} = - 2$

$\frac{90 - x}{- x} = - 2 \Rightarrow 90 - x = 2 x \Rightarrow x = 30$

u=-30 cm, v=+60 cm

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{60} - \frac{1}{- 30} = \frac{3}{60} = \frac{1}{20} \Rightarrow f = 20 cm$

Q-2.An image formed by a convex lens is upright and four times the size of the object. Given the focal length of the lens is 20 cm,Find the object and image distances.

Solution:

To calculate u

$m = \frac{f}{f + u} \Rightarrow 4 = \frac{20}{u + 20} \Rightarrow u = - 15 cm$

To calculate v

$m = \frac{f - v}{f} \Rightarrow 4 = \frac{20 - v}{20} \Rightarrow v = - 60 cm$

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Convex Lens

It is a transparent optical device that converges light rays passing through it to a single point called the focal point. It is thicker at the center than at the edges and is commonly used to form real or magnified images. Convex lenses are found in everyday objects like eyeglasses, magnifying glasses, and cameras. They come in different types, including plano-convex and double-convex lenses, and are essential in optical systems due to their ability to focus light.

1.0Definition of Convex Lens

A lens is a portion of a transparent material with two refracting surfaces such that at least one is curved with the refractive index of its material being different from that of the surroundings.
A thin spherical lens with refractive index greater than that of surroundings behaves as a convergent or convex lens, i.e., converges parallel rays if its central (i.e. paraxial) portion is thicker than marginal one.

2.0Types of Convex Lens

3.0Principal Focus of Convex Lens

Principal Focus: A Lens has two focal points.

First Focus: First focal point is an object point on the principal axis corresponding to which the image is formed at infinity.

Second Focus: Second focal point is an image point on the principal axis corresponding to which object lies at infinity.

4.0Rules For Image Formation In Convex Lens

A ray passing through the optical centre proceeds without deviation through the lens.
A ray passing through first focus or directed towards it, becomes parallel to the principal axis after refraction from the lens.
A ray passing parallel to the principal axis passes or appears to pass through F after refraction through the lens.

5.0Image Formation In Convex Lens

6.0Image formation in Convex Lens

Position of Object- Placed at Infinity
Position of Image-Formed at f
Nature-Real, Inverted
Size-Highly Diminished

Position of Object- Placed at -∞ and 2f
Position of Image-Formed in between 2f and f
Nature-Real,Inverted
Size- Diminished

Position of Object- Placed at -2f
Position of Image-Formed at 2f
Nature-Real,Inverted
Size- Equal in size

Position of Object- Placed in between -2f and -f
Position of Image-In between 2f and ∞
Nature-Real,Inverted
Size- Enlarged

Position of Object- Placed in between -2f and -f ( very nearer to -f)
Position of Image-Formed At ∞
Nature-Real,Inverted
Size- Enlarged

Position of Object- Object is Placed in between -f and optical centre ( very nearer to -f)
Position of Image-Formed At - ∞
Nature-Virtual,Erect
Size- Highly Enlarged

Position of Object- Object is Placed in between -f and optical centre
Position of Image-In between - ∞ and Optical Centre
Nature-Virtual,Erect
Size- Enlarged

7.0Lens Formula For Convex Lens

Object AB is positioned between the optical centre and and focus of the convex lens.Image A’B’ formed by convex lens is virtual,erect and magnified.

$Δ A^{'} B^{'} O and A BO are similar$

$\frac{A ^{'} B ^{'}}{A B} = \frac{B ^{'} O}{B ^{'} O}$ ……….(1)

$Δ A^{'} B^{'} F and MOF$ are similar

$\frac{A ^{'} B ^{'}}{MO} = \frac{BF}{OF}$

MO=AB therefore

$\frac{A ^{'} B ^{'}}{A B} = \frac{BF}{OF}$ ……….(2)

$\frac{- v}{- u} = \frac{- f + v}{- f}$

$v f = u f - uv \Rightarrow uv = u f - v f$

Dividing both sides by uvf we get

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

8.0Magnification for Convex Lens

It is defined as the ratio of the size of image formed by the lens to the size of the object.

$m = \frac{Size of Image}{Size of Object} = \frac{h _{2}}{h _{1}} = \frac{v}{u}$

Linear Magnification in terms of u and f

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

Multiplying both sides by u

$\frac{u}{v} - 1 = \frac{u}{f} \Rightarrow \frac{u}{v} = \frac{f + u}{f}$

$m = \frac{1}{u} = \frac{f}{f + u}$

Linear Magnification in terms of v and f

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

Multiplying both sides by v

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

$m = \frac{v}{u} = \frac{f - v}{f}$

Example-1.An object and a screen are positioned 90 cm apart. What is the required focal length and type of lens needed to form a distinct image on the screen, two times the the size of the object?

Solution:Since the image is real, a convex lens should be placed between the object and the screen.

u=-x

v=90-x

$m = \frac{v}{u} = - 2$

$\frac{90 - x}{- x} = - 2 \Rightarrow 90 - x = 2 x \Rightarrow x = 30$

u=-30 cm, v=+60 cm

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{60} - \frac{1}{- 30} = \frac{3}{60} = \frac{1}{20} \Rightarrow f = 20 cm$

Q-2.An image formed by a convex lens is upright and four times the size of the object. Given the focal length of the lens is 20 cm,Find the object and image distances.

Solution:

To calculate u

$m = \frac{f}{f + u} \Rightarrow 4 = \frac{20}{u + 20} \Rightarrow u = - 15 cm$

To calculate v

$m = \frac{f - v}{f} \Rightarrow 4 = \frac{20 - v}{20} \Rightarrow v = - 60 cm$

Frequently Asked Questions

What happens to parallel rays of light when they pass through a convex lens?

How does the image formed by a convex lens change as the object distance increases?

Can a convex lens produce a virtual image?

What separates a real image from a virtual image created by a convex lens?

How does the curvature of a convex lens affect its focal length?

Join ALLEN!

Convex Lens

1.0Definition of Convex Lens

2.0Types of Convex Lens

3.0Principal Focus of Convex Lens

4.0Rules For Image Formation In Convex Lens

5.0Image Formation In Convex Lens

6.0Image formation in Convex Lens

7.0Lens Formula For Convex Lens

8.0Magnification for Convex Lens

Table of Contents

Frequently Asked Questions

What happens to parallel rays of light when they pass through a convex lens?

How does the image formed by a convex lens change as the object distance increases?

Can a convex lens produce a virtual image?

What separates a real image from a virtual image created by a convex lens?

How does the curvature of a convex lens affect its focal length?

Join ALLEN!

Convex Lens

1.0Definition of Convex Lens

2.0Types of Convex Lens

3.0Principal Focus of Convex Lens

4.0Rules For Image Formation In Convex Lens

5.0Image Formation In Convex Lens

6.0Image formation in Convex Lens

7.0Lens Formula For Convex Lens

8.0Magnification for Convex Lens

Table of Contents