Question

what is lens maker formula and its expression

Answer 1

sing the positive optical sign convention, the lens maker's formula states

where f is the focal length, n is the index of refraction, and  and  are the radii of curvature of the two sides of the lens.. Lens maker formula is used to construct a lens with specified focal length. A lens has two curved surfaces, but both are not exactly same. If the refractive index and the radius of curvature of both the surface are known, you can determine the focal length of that particular lens by using the given lens maker’s formula,

Where,

f = focal length of the lens,

μ = refractive index of the material,

R1 and R2 = radius of curvature of both surfaces.

Example 1:

Determine the focal length of the lens whose refractive index and radius of curvature of each surface are 2, 20cm and -35cm respectively.

Answer 2

 



Shirin Siddiqui asked in Science

How can we derive the formulae for the lens ie 1/f = 1/v + 1/u ?

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Vijay.yadav... answered this
2049 helpful votes in Science, Class XII-Science

Hello,

This lens formula given by 



To derive first we go through refraction through the spherical refracting surface.

A refracting surface which forms a part of a sphere of transparent refracting material is called a spherical refracting surface.



The above figure shows the geometry of formation of image I of an object O and the principal axis of a spherical surface with centre of curvature C and radius of curvature R.

Assumptions:

(i) The aperture of the surface is small compared to other distance involved.

(ii) NM will be taken to be nearly equal to the length of the perpendicular from the point N on the principal axis.



For ΔNOC, i is the exterior angle.

∴ i = ∠NOM + ∠NCM



Similarly, r = ∠NCM − ∠NIM

i.e.,

By Snell’s law,

n1 sini = n2 sinr

For small angles,

n1i = n2 r

Substituting the values of i and r from equations (i) and (ii), we obtain



Applying new Cartesian sign conventions,

OM = − u, MI = + v, MC = + R

Substituting these in equation (iii), we obtain



This equation holds for any curved spherical surface.