Apply lens makers formula for different types of lenses.
Answers
Lens manufacturers use the lens maker’s formula to manufacture lenses of the desired focal length. Lenses of different focal length are used for different optical instruments. The focal length of a lens depends on the refractive index of the lens and the radii of curvature. The lens maker’s equation is another formula used for lenses that give us a relationship between the focal length, refractive index, and radii of curvature of the two spheres used in lenses.
The lens maker’s equation for thin lenses is as given below as;
1f = (n−1)(1R1 − 1R2)
where,
f is the focal length (half the radius of curvature)
n is the refractive index of the material used
R1 is the radius of curvature of sphere 1
R2 is the radius of curvature of sphere 2
As previously mentioned, this equation can be used only for thin lenses. Lenses where the thickness is lesser, such that they are considered negligible in comparison to the radius of curvature, are referred to as thin lenses.
If the thickness of lens has to be considered in comparison to the radius of curvature, the following lens formula for thick lenses can be used.
1f = (n−1)[1R1 − 1R2 + (n−1)dn×R1×R2]
where,
d is the thickness of the lens in consideration.
Another situation which has to be considered is the lens maker’s formula accounting for objects that are present in different media. The equation is as follows,
1f=[n1n2 − 1] × [R1 − R2R1 × R2]
where,
n1 is the refractive index of the lens in consideration
n2 is the refractive index of the medium outside
Have you asked yourself this question? “What is the significance of ignoring the thickness sometimes and considering it sometimes?”
Well, the answer to that is when the light ray travels from a medium of, say air, to the medium of the lens, it undergoes refraction. But when it travels from the medium of the lens to that of the air, it undergoes refraction again. The double refraction can be ignored if the lenses in optics are thin enough to make the assumption that light is refracted only once. This is done to make ray optics calculations simpler, but the first step would be to identify what constitutes thin and thick lenses.
Limitations of Lens Maker’s Formula
The lens needs to be thin. This is because the separation between the two refracting surfaces will also be small.
The medium on either side of the lens needs to be the same.
On violation of any of the limitation then the refraction at the curved surface formula is used for both the surfaces.
Helpful Sign Conventions
For a Convex (converging) Lens
R1 = positive
R2 = negative
f = positive
For a Concave (diverging) Lens
R1 = negative
R2 = positive
f = negative