Question

derive lens formula​

Answer 1

Explanation:

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.

Answer 2

Answer:

• The figure above shows that formation of a real, inverted and diminished image A'B' of the object AB placed beyond the centre of curvature at a distance u from the convex lens. ...
• According to Cartesian sign convention,
• Object distance (OB) = -u.
• Image distance (OB') = +v.
• Focal length (OF1 = OF2) = +f.