How To Use LENS MAKER FORMULA : Sign Convention and LENS NUMERICALS: Class X :ICSE /CBSE PHYSICS
Summary
TLDRThe 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
🔍 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.
📏 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.
📚 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.
Mindmap
Keywords
💡Lens Maker Formula
💡Focal Length
💡Convex Lens
💡Concave Lens
💡Optical Center
💡Object Distance
💡Image Distance
💡Positive Direction
💡Principal Axis
💡Sign Convention
💡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
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