How To Use LENS MAKER FORMULA : Sign Convention and LENS NUMERICALS: Class X :ICSE /CBSE PHYSICS

Summary

The video script offers a detailed explanation of the lens maker formula, crucial for determining image positions in lenses. It emphasizes four key rules: a convex lens has a positive focal length, a concave lens has a negative one; all distances are measured from the optical center; distances in the direction of incident light are positive; and heights above the principal axis are positive. A practical example demonstrates applying these rules to find the image position for a convex lens with a 10 cm focal length and an object placed 20 cm away, resulting in an image 20 cm from the optical center on the positive side.

Takeaways

• 🔍 The Lens Maker Formula is given by 1/f = 1/V - 1/U, where f is the focal length, V is the image distance, and U is the object distance.
• 🌟 For a convex lens, the focal length (f) is always positive, while for a concave lens, it is always negative.
• 📏 All distances, whether object or image distance, are measured from the optical center of the lens.
• 📍 The direction of the incident light determines the positive direction for distance measurements in lens problems.
• 📈 Heights measured above the principal axis are considered positive, while those below are negative.
• 📚 Understanding the four rules is essential for solving any lens-related problem using the Lens Maker Formula.
• 🔄 The formula is used to find the position of the image formed by lenses when the object is placed at different positions.
• 👉 In the example given, a convex lens with a focal length of 10 cm is used, and the object is placed 20 cm from the lens.
• ➡️ The object distance (U) is considered negative in the formula because it is in the positive direction from the optical center.
• 🔢 By applying the Lens Maker Formula, the image distance (V) is calculated to be 20 cm from the optical center in the positive direction.
• 🖼️ The image is formed at the same distance from the lens as the object but on the opposite side, indicating a real image.

Q & A

What is the lens maker formula?

The lens maker formula is given by 1/f = 1/v - 1/u, where 'f' is the focal length of the lens, 'v' is the image distance, and 'u' is the object distance.

What is the significance of the lens maker formula in optics?

The lens maker formula is used to determine the position of the image formed by a lens when an object is placed at different positions relative to the lens.

What are the two types of lenses mentioned in the script, and how do they form images differently?

The two types of lenses mentioned are convex and concave lenses. Convex lenses converge light and typically form real, inverted images, while concave lenses diverge light and usually form virtual, upright images.

Why is the sign of the focal length important in the lens maker formula?

The sign of the focal length is crucial as it indicates the type of lens: a positive sign for a convex lens and a negative sign for a concave lens, which affects the calculation of image positions.

What are the four rules for applying the lens maker formula as outlined in the script?

The four rules are: 1) The focal length of a convex lens is always positive, and for a concave lens, it is always negative. 2) All distances are measured from the optical center. 3) Distances measured in the direction of incident light are positive. 4) Heights above the principal axis are positive, while those below are negative.

Why is the optical center important when measuring distances in the lens maker formula?

The optical center is the reference point from which all distances (object distance 'u' and image distance 'v') are measured in the lens maker formula, ensuring consistency and accuracy in calculations.

How does the direction of incident light affect the calculation of distances in the lens maker formula?

The direction of incident light determines the positive direction for distance measurements. Distances measured in the direction of the incident light are considered positive, while those in the opposite direction are negative.

What does the principal axis represent in the context of the lens maker formula?

The principal axis is a reference line that passes through the optical center of the lens. Heights above this axis are considered positive, while those below are negative in the lens maker formula.

Can you provide an example of how to use the lens maker formula with a convex lens?

Sure. Given a convex lens with a focal length of 10 cm and an object placed 20 cm from the lens, you would use the formula 1/f = 1/v - 1/u, where f = 10 cm (positive), u = -20 cm (negative because the object is in the positive direction), and solve for 'v' to find the image distance.

What is the image distance if a convex lens with a 10 cm focal length is used and the object is placed 20 cm from the lens?

Following the rules and applying the lens maker formula, the image distance 'v' would be calculated as 20 cm in the positive direction, meaning the image is formed 20 cm from the optical center on the same side as the object.

How does the height above or below the principal axis affect the calculation in the lens maker formula?

Heights measured above the principal axis are considered positive, while those below are negative. This is important for calculating the position of the image, especially when the object is not aligned with the principal axis.

Outlines

00:00

🔍 Understanding the Lens Maker Formula

The video script begins by introducing the lens maker formula, which is essential for determining the position of an image formed by a lens. The formula is given as 1/f = 1/V - 1/U, where f is the focal length, V is the image distance, and U is the object distance. The script explains that the formula is applicable to both convex and concave lenses, which form different types of images. It emphasizes the importance of understanding the formula's application and the rules for determining the signs of f, V, and U. The first two rules are presented: the focal length of a convex lens is always positive, and the focal length of a concave lens is negative. All distances are measured from the optical center, which may be inside or outside the lens but is typically considered to be inside at the high school level.

05:02

📏 Applying the Lens Maker Formula with Rules

This paragraph continues the explanation of the lens maker formula by outlining the remaining rules for its application. Rule number three states that all distances measured in the direction of the incident light are considered positive. The direction of the incident light determines the positive direction, which can vary depending on the light's path. Rule number four specifies that any height above the principal axis is positive, while any height below it is negative. The script then applies these rules to a practical problem involving a convex lens with a 10 cm focal length and an object placed 20 cm from the lens. The object distance U is determined to be negative because it is in the positive direction from the optical center. The formula is then used to calculate the image distance V, resulting in an image formed 20 cm from the optical center in the positive direction.

10:06

📚 Conclusion of the Lens Maker Formula Application

The final paragraph of the script concludes the application of the lens maker formula by summarizing the outcome of the example problem. It confirms that the image is formed 20 cm from the optical center in the positive direction, which is consistent with the rules previously discussed. The script visually describes the path of the light from the object to the lens and the formation of the image, reinforcing the understanding of the lens maker formula and its practical application. The summary serves to clarify the process and ensure that the viewer has a clear understanding of how to apply the formula in various scenarios.

Keywords

💡Lens Maker Formula

The Lens Maker Formula is a fundamental equation in optics used to calculate the position of an image formed by a lens. It is expressed as \( \frac{1}{f} = \frac{1}{V} - \frac{1}{U} \), where \( f \) is the focal length of the lens, \( V \) is the image distance, and \( U \) is the object distance. The formula is central to the video's theme of understanding lens behavior, as it is used to determine how images are formed at different positions when the object is placed at varying distances from the lens.

💡Focal Length

Focal length is the distance from the center of a lens to the point where parallel rays of light converge after passing through the lens. It is a critical parameter in the Lens Maker Formula and is represented by \( f \). In the context of the video, the focal length is essential for determining the nature of the image formed by the lens, with a positive value for a convex lens and a negative value for a concave lens.

💡Convex Lens

A convex lens, also known as a converging lens, bulges outward and is capable of focusing light rays to a point. In the video, the convex lens is described as having a positive focal length, which means it can form real, inverted images. The script uses the convex lens as an example to demonstrate the application of the Lens Maker Formula.

💡Concave Lens

A concave lens is thinner at the center than at the edges and causes light rays to diverge. Unlike a convex lens, a concave lens has a negative focal length, which means it forms virtual, upright images. The video script mentions concave lenses to contrast with convex lenses and to explain the sign convention for focal lengths.

💡Optical Center

The optical center, also referred to as the 'O' in the script, is the central point of a lens from which distances are measured. It is crucial for determining the object and image distances in the Lens Maker Formula. The script emphasizes that all distances should be measured from the optical center, which is typically located within the lens at the high school level.

💡Object Distance

Object distance (\( U \)) is the distance from the object to the optical center of the lens. In the video, object distance is used in the Lens Maker Formula to calculate the position of the image. The script clarifies that object distance should be measured from the optical center and can be positive or negative depending on the direction of the incident light.

💡Image Distance

Image distance (\( V \)) is the distance from the image to the optical center of the lens. The video script uses the Lens Maker Formula to find the image distance when the object distance and focal length are known. The sign of the image distance indicates whether the image is real (positive) or virtual (negative).

💡Positive Direction

The positive direction in the script refers to the direction from which the incident light is coming. It is essential for determining the sign of the object and image distances in the Lens Maker Formula. The script explains that the direction of the incident light is considered positive, and the opposite direction is negative.

💡Principal Axis

The principal axis is an imaginary line passing through the optical center of the lens. It serves as a reference for measuring distances and heights in lens problems. The script mentions the principal axis when explaining the sign convention for heights above and below it, with heights above being positive and those below being negative.

💡Sign Convention

Sign convention is a set of rules used to determine whether a quantity is positive or negative in optics problems. The video script outlines four rules for the Lens Maker Formula, including the sign conventions for focal lengths, distances measured from the optical center, distances in the direction of incident light, and heights above the principal axis.

💡Real Image

A real image is formed when the light rays actually converge at a point after passing through the lens. The script explains that a convex lens with a positive focal length can form a real image, as demonstrated in the example problem where the image distance is calculated to be a positive value, indicating a real image.

Highlights

Introduction to the lens maker formula and its application in finding image positions in lenses.

Explanation of the lens maker formula: 1/f = 1/V - 1/U, where f is the focal length, V is the image distance, and U is the object distance.

Different types of lenses: convex and concave, and how they form different kinds of images.

Understanding when to use positive or negative values for focal lengths (convex positive, concave negative).

Rule one: The focal length of a convex lens is always positive.

Rule two: The focal length of a concave lens is always taken as negative.

Rule three: All distances are measured from the optical center of the lens.

Clarification on the optical center's location and its importance in measuring distances.

Rule four: Distances measured in the direction of the incident light are considered positive.

The concept of the principal axis and its role in determining the direction of positive and negative distances.

Rule five: Heights above the principal axis are positive, while those below are negative.

Application of the lens maker formula to a problem involving a convex lens with a focal length of 10 cm and an object placed 20 cm from the lens.

Step-by-step calculation to find the image distance using the lens maker formula.

Determining the direction of the incident light to ascertain the positive direction for distance measurements.

Final calculation resulting in an image distance of 20 cm from the optical center in the positive direction.

Visual representation of light rays and the formation of the image through the lens.

Conclusion emphasizing the clarity and simplicity of applying the lens maker formula to practical problems.

Transcripts

foreign

how to apply the lens maker formula the

lens maker formula is 1 by f is equals

to 1 by V minus 1 by U

okay this is used to find the position

of image in lenses so f is over here the

focal length

focal length

we is the image distance

and U is object distance

okay

so we all know that images are formed by

lenses at different positions when the

object is placed at different positions

so basically you have two kind of

kind of convex lens and concave length

and both form different kind of images

but how to use this formula for lenses

is very important

you've got to understand how to apply

this formula

and when is f positive or negative and

similar for V and u

so there are basically four rules

remember just four rules I am going to

tell you and those four rules will be

sufficient to solve any lens related

problem any any lens related problem

rule number first

the focal length for a convex lens

for a convex lens is always positive

convex lens focal length always positive

and the focal length for a concave lens

will always be taken as negative okay

convex positive and concave negative

clear okay rule number two

all distance

all distance

are measured

from

o

what is o

the optical center

yes

Optical

Center or hamisha optical center yes

not necessary no no it's not necessary

optical center can also lie outside lens

but again at high school level it will

always be inside the lens so the second

rule is whether you measure image

distance whether you measure object

distance but from where from optical

center

these two rules

keep in your mind

all distance are measured from optical

center when you have to measure image

you will measure image distance from

optical center from from

okay it is not the distance between it

is the distance from okay and similarly

for object distance

so two rules are over here

and I must write the rule number three

distance

measured

in

Direction

of

incident

light

are

positive

so in any physics problem

which is related to distance or

displacement

we must always be sure

that which direction is the positive

direction

so for lenses the direction of incident

light

the direction of incident light yes be

very sure about direction of incident

light

from which direction light is coming

that direction is positive suppose the

light is coming like this so this

direction will become positive and this

will be negative and if the light is

coming like this this direction will be

positive so there are no fixed positive

or negative Direction it depends upon

direction of incident light

so we have one two three rules rule

number one cosmic's lens focal length

positive rule number two concave length

focal length negative this is rule

number one only

then rule number two all distance are

measured from optical center what is

optical center suppose this is lens this

is optical center this is lens then this

is optical center

and rule number three all distance

measured in the direction of incident

light are positive

so there is one rule left that is Rule

Number Four and rule number four states

Rule Number Four

height

above

principle

axis

are positive

okay

suppose this is the principal axis

so any height above it will be positive

and any height below it

below the principal axis this is

principal axis any height below it will

be taken as negative

these are the four rules keep in mind

now let's try

to apply this rule

to a simple problem

okay

so the question reads

suppose

we have

a convex lens okay so we have a convex

lens

whose focal length is 10 centimeter

and an object

is placed

20 centimeter

from lens

find

position

of

image

okay

so we have one convex lens

and this is the principal axis

and the focal length is 10. now remember

for convex length the focal length will

be plus 10.

and the object is placed over here this

is the object

at a distance of 20 centimeter from the

lens from the optical center

now where is the image formed

so light will be coming from the object

yes

light will be coming from object towards

the lens

and then light will refract and image

will form

so this is our incident light

yes incident light

so now we are sure that this direction

will be treated as positive the

direction of incident Ray is the

positive direction

now let us try to

see what is f plus 10 what is u u is

object distance

all distance are measured from optical

center so from optical center the object

is 20 centimeter away

so U is 20 centimeter

but wait

whether it is positive or negative

see

this direction is positive

and object is in this direction because

all distance are measured from optical

center like this

so this direction will be negative so U

is minus 20.

now we need to find position of image

that is V

let us apply the Formula 1 by f is

equals to 1 by B minus 1 by U

so 1 by 10 is equals to 1 by V minus 1

by minus 20.

so we'll get 1 by V is equals to 1 by 10

plus 1 by 20 LCM will be 22 plus 1 that

is

that is

that is 3 by 20 is it so is it so plus

20 this size will be minus okay sorry so

this will be 1 by B is equals to 1 by 10

minus 1 by 20 this will be plus and when

this will go to this direction will be

negative

so it will be 22 minus 1 so we get 1 by

20.

1 by V 1 by 20 so V is

20 centimeter

plus 20 centimeter

so the image distance is 20 centimeter

from where from the optical center

and see V is positive 20.

so this is the positive direction

so the image is formed at a distance of

20 centimeter from optical center

where in the positive direction

over here is the image formed the

resistance of 20 centimeter

ok so the light goes like this and then

comes like this and one light goes

through optical center

and here is the image formed

clear so simple