Lines and optical instruments

Содержание и основные понятия

The lens draws parallel rays into a focus that disperses them. The position and size of the image vary from the distance of the object to the lens.
GEF · Grade 8
PIF · Baseline
Interactive model
lens
Focus
optical force
actual image
Imperson image
01
The physical picture
What happens and what boundaries the model has.
Main message
The lens draws parallel rays into a focus that disperses them. The position and size of the image vary from the distance of the object to the lens.
The optical force is equal to the amount, reverse focus distance in metres.
Two distinct rays are enough to build.
The eye, camera, lupa, and projector use lenses, but get images of different uses.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
D
=
1
F
D=\frac{1}{F}
D
=
F
1
​
optical force
1
F
=
1
d
+
1
f
\frac{1}{F}=\frac{1}{d}+\frac{1}{f}
F
1
​
=
d
1
​
+
f
1
​
thin lens formula
Review of the situation
The object behind the double focus of the collecting lens gives a reduced inverted real image between F and 2F.
04
Links and application
In the real world
The object behind the double focus of the collecting lens gives a reduced inverted real image between F and 2F.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Lins and optical instruments" through the model, not just through the formula.
Outcome 2
Clear and correct use of terms: lens, focus, optical force.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
lens
A transparent body with refracting surfaces that form a sliding beam or a split beam.
Focus
The point at which parallel rays are collected or from which they appear to be coming out.
optical force
The value of the backward focal distance of the lens in metres is measured in dioptriles.
actual image
Image created by a real intersection of luminous beams, allowing for receipt on screen.
Imperson image
Image at intersection points with continued beams which cannot be directly obtained on the screen.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
D
=
1
F
D=\frac{1}{F}
D
=
F
1
​
definition
Optimal power.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
F
=
фокусное расстояние линзы
F=\text{фокусное расстояние линзы}
F
=
Focus
distance
lenses
The magical distance is the marked distance to the main focus: the collecting lens has paraxial rays in it, and the diffuser has a cross-section of their backsliding.
D
=
1
F
D=\frac{1}{F}
D
=
F
1
​
The wholesale force is introduced as the reverse focus distance in metres; the smaller ,F, corresponds to the stronger lens.
Conditions:
The thin lens in the given environment; F is expressed in metres, the F sign is positive for the collecting lens and negative for the lens.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
1
F
=
1
d
+
1
f
\frac{1}{F}=\frac{1}{d}+\frac{1}{f}
F
1
​
=
d
1
​
+
f
1
​
model effect
A thin lens formula.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
h
′
h
=
f
d
\frac{h'}{h}=\frac{f}{d}
h
h
′
​
=
d
f
​
A similar triangle for the beam through the optical center connects the increase to the distance to the object and the image.
h
′
h
=
f
−
F
F
\frac{h'}{h}=\frac{f-F}{F}
h
h
′
​
=
F
f
−
F
​
The likeness of triangles for a beam running parallel to the axis and passing through the focus gives a second connection.
f
d
=
f
−
F
F
⇒
1
F
=
1
d
+
1
f
\frac{f}{d}=\frac{f-F}{F}\Rightarrow\frac{1}{F}=\frac{1}{d}+\frac{1}{f}
d
f
​
=
F
f
−
F
​
⇒
F
1
​
=
d
1
​
+
f
1
​
The equality of two expressions for a linear increase results in the lens formula.
Conditions:
This geometric conclusion refers to the collection of a thin lens with an actual object and image; d > 0, f > 0 and F > 0; and h and hʹ refer to height modules. For imaginary images and diffuse lenses, it is necessary to make a separate sign agreement.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't change the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that the optical force is equal to the amount, the reverse focus distance in metres.
How to Check the Mind
Two characteristic rays are sufficient to build. Then check the units, vector direction and the behaviour of the result at zero or very large parameter.
Σ
Conclusion on the topic
Lines and optical instruments
The lens draws parallel rays into a focus that disperses them. The position and size of the image vary from the distance of the object to the lens.
The optical force is equal to the amount, reverse focus distance in metres.
Two distinct rays are enough to build.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.