drive lens formula for convex lens when real image formed.
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Answer:
What is Lens Formula?
In optics, the relationship between the distance of an image (v), the distance of an object (u), and the focal length (f) of the lens is given by the formula known as Lens formula. Lens formula is applicable for convex as well as concave lenses. These lenses have negligible thickness. The formula is as follows:
1v−1u=1f
Lens Formula Derivation
Consider a convex lens with an optical center O. Let F be the principle focus and f be the focal length. An object AB is held perpendicular to the principal axis at a distance beyond the focal length of the lens. A real, inverted magnified image A’B’ is formed as shown in the figure.
From the given figure, we notice that △ABO and △A’B’O are similar.
Therefore,
A′B′AB=OB′OB (1)
Similarly, △A’B’F and △OCF are similar, hence
A′B′OC=FB′OF
But, OC=AB
Hence,
A′B′AB=FB′OF (2)
Equating eq (1) and (2), we get
OB′OB=FB′OF=OB′−OFOF
Substituting the sign convention, we get
OB=-u, OB’=v and OF=f
v−u=v−ff
vf=−uv+uforuv=uf−vf
Dividing both the sides by uvf, we get
uvuvf=ufuvf−vfuvf
⇒1f=1v−1u
The above equation is known as the Lens formula.
This was the derivation of Lens formula. Stay tuned with BYJU’S and learn various other Physics related topics.
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Explanation:
Descartes
Figure 78: A thin lens. is the refractive index of the lens. The above formula is usually called the lens-maker's formula, and was discovered by Descartes. Note that the lens-maker's formula is only valid for a thin lens whose thickness is small compared to its focal length.
Answer:
According to the convex lens equation, 1/f = 1/v + 1/u. It relates the focal length of a lens with the distance of an object placed in front of it and the image formed of that object.