Now as we know that:
We get:
► tanα = MN / OM
► tanγ = MN / MC
► tanβ = MN / MI
Now, for Δ NOC, i is the exterior angle.
i = ∠ NOM + ∠ NCM
i= MN / OM + MN / MC ...(1)
Similarly,
r = MN / MC – MN / MI ...(2)
Now by using Snell’s law we get:
n_{1} sin i = n_{2}sin r
Substituting i and r from Eq. (1) and (2), we get
n_{1 }/ OM + n_{2 }/ MI = (n_{2 }− n_{1}) / MC
As, OM = u, MI = +v, MC = +R
Hence, the equation becomes:
A lens is a uniform transparent medium bounded between two spherical or one spherical and one plane surface.
Here are some terms related to Lens:
➢ Lens Formula
1/f = 1/v – 1/u
where, f = focal length of the lens, U = distance of object, U = distance of image.
Lens Maker’s formula
1/f=(μ – 1) (1/R_{1} – 1/R_{2})
where, μ = refractive index of the material of the lens and R_{1} and R_{2} are radii of curvature of the lens.
➢ Power of a Lens
The reciprocal of the focal length of a lens, when it is measured in metre, is called power of a lens.
Power of a lens, (P)= 1/f(metre)
Its unit is dioptre (D).
The power of a convex (converging) lens is positive and for a concave (diverging) lens it is negative.
➢ Focal Length of a Lens Combination
(i) When lenses are in contact 1/F – 1/f_{1} + 1/f_{2}
Power of the combination P = P_{1} + P_{2}
(ii) When lenses are separated by a distance d
1/F = 1/f_{1} + 1/f_{2} – d/f_{1}f_{1}
Power of the combination:
P = P_{1} + P_{2} – dP_{1}P_{2}
➢ Linear Magnification
m = I/O = v/u
For a small sized object placed linearly along the principal axis, its axial (longitudinal) magnification is given by
Axial magnification = – dv/du = (v/u)^{2}
= (f / f+u)^{2} = (f  v/f)^{2}
➢ Focal Length of a Convex Lens by Displacement Method
Focal length of the convex lens f = (a^{2} – d^{2}) / 4a
where, a = distance between the image pin and object pin and
d = distance between two positions of lens.
The distance between the two pins should be greater than four times the focal length of the convex lens, i.e., a > 4f.
Height of the object O = √I_{1}I_{2}
➢ Cutting of a Lens
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1. What is refraction at a spherical surface? 
2. What are the types of lenses? 
3. How does refraction occur at a spherical lens? 
4. What are some applications of refraction in lenses? 
5. How can I calculate the refractive power of a lens? 

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