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As shown in figure the centre of the lens is denoted as C and the principal axis is X'X. The R1 and R2 are the radii of the curvature of the surfaces of lens and the poles are P1 and P2. The variable t represents the thickness of the lens which has the small value. The object in principal axis is O. The distance between the point object and the pole P1 is u. The image of point object O is refracted at I which has the distance v' from the pole P1.
Based on the refraction formula of the spherical surface,
- =
In second surface the virtual object is denoted as I' after completion of refraction the final complete image should be created at I. The distance between the final object I and the pole is v. The distance between the virtual object I' and the pole P2 is (v'-t).
If there is refraction at second medium then the ray is moving from the second medium to first medium.
Derivation of Lens-maker's Formula:Refraction formula,- = -----------------------------(1)
Here the value of t is negligible because it has very small value. Therefore the equation becomes
- = - --------------------------------(2)
By adding the equations (1) and (2) we get,
- =
=
=
Where the refractive index of the second medium is denoted as which is related to the first medium.
When the object is at infinity, the image should be created at second focus. That is u=∞, v=f2=f.
=
Therefore refraction formula for thin lens:
=
Which is known as Lens-Maker's formula.
Consider the air is the first medium and n be the refractive index of the material. In this
Now the derivation of Lens-Maker's formula is,
= (n-1)
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What is the derivation of lens maker formula?
Derivation of Lens-maker's Formula:Derivation of Lens-Maker's formula: As shown in figure the centre of the lens is denoted as C and the principal axis is X'X. The R1 and R2 are the radii of the curvature of the surfaces of lens and the poles are P1 and P2. The variable t represents the thickness of the lens which has the small value. The object in principal axis is O. The distance between the point object and the pole P1 is u. The image of point object O is refracted at I which has the distance v' from the pole P1.Based on the refraction formula of the spherical surface,- =In second surface the virtual object is denoted as I' after completion of refraction the final complete image should be created at I. The distance between the final object I and the pole is v. The distance between the virtual object I' and the pole P2 is (v'-t).If there is refraction at second medium then the ray is moving from the second medium to first medium.Derivation of Lens-maker's Formula:Refraction formula, - = -----------------------------(1)Here the value of t is negligible because it has very small value. Therefore the equation becomes- = - --------------------------------(2)By adding the equations (1) and (2) we get,- ===Where the refractive index of the second medium is denoted as which is related to the first medium.When the object is at infinity, the image should be created at second focus. That is u=∞, v=f2=f.=Therefore refraction formula for thin lens:=Which is known as Lens-Maker's formula.Consider the air is the first medium and n be the refractive index of the material. In thisNow the derivation of Lens-Maker's formula is,= (n-1)
Which type of lens is used by watch maker?
The small magnifying lens used by jewelers and watchmakers is a loupe.
What is the lens maker's formula and how is it used to calculate the focal length of a lens?
The lens maker's formula is a mathematical equation used to calculate the focal length of a lens based on its refractive index and the radii of curvature of its surfaces. It is expressed as: 1/f (n - 1) (1/R1 - 1/R2) Where: f focal length of the lens n refractive index of the lens material R1 radius of curvature of the first lens surface R2 radius of curvature of the second lens surface By plugging in the values for n, R1, and R2 into the formula, one can determine the focal length of the lens.
Apart from newton and galileo who else invented a telescope?
Hans Lippershey, who was a German lens maker
What is the lens maker formula and how is it used to calculate the focal length of a lens?
The lens maker formula is a mathematical equation used to calculate the focal length of a lens based on its refractive index and the radii of curvature of its surfaces. It is expressed as: 1/f (n - 1) (1/R1 - 1/R2) Where: f is the focal length of the lens n is the refractive index of the lens material R1 is the radius of curvature of the first lens surface R2 is the radius of curvature of the second lens surface By plugging in the values for n, R1, and R2 into the formula, you can calculate the focal length of the lens. This formula is essential for lens designers and manufacturers to ensure that lenses have the desired optical properties for various applications.
How did Hans lippershey discover the microscope?
He discovered it by when he was a lens-maker back then when his kids were playing outside the that was the time when he discovered it
Derivation programming language grammar.?
wht is the derivation of little
What is the derivation of x2?
Derivation of x2 or 2x is 2.
Where did the hand lens were created?
The hand lens was invented in the 17th century by Dutch spectacle maker, Zacharias Janssen. He created the first compound microscope by combining lenses in a tube to magnify small objects.
Derivation of pedal curve in cartesian coordinates?
derivation of pedal equation
Who invented the first hand lens?
William Julliano invented the first hand lens in 1991
What is a word for the derivation of a word from a name?
Eponymy is the derivation of a word from a name.
