Optical Physics Homework Help: Lenses
1. Principle focus: when a beam of light is incident on a lens in a direction parallel to the principle axis of the lens, the rays after refraction through the lens converge to (in case of convex lens) or appear to diverge (in case of concave lens) from a point on the principle focus of the lens.
CF = ƒ is principle focal length of the lens.
2. Aperture: aperture of a lens is the effective diameter of its light transmitting area. Therefore, according to homework service the brightness i.e. intensity of image formed by a lens-which depends on the amount of light passing through the lens will vary as square of the aperture of the lens i.e. I ∝ (aperture)2
Lens maker formula
Lens maker’s formula is a relation that connects focal length of a lens to radii of curvature of two surfaces of the lens and refractive index of the material of the lens.
It is useful to design lenses of desired focal length using suitable material and surfaces of suitable radii of curvature.
In deriving this formula, we use New Cartesian sign conventions:
1. All the distances are measured from the optical centre of the lens.
2. All the distances measured in the direction of incidence of light are taken as positive, whereas all the distances measured in a direction of incidence of light are taken as negative.
3. For a convex lens, ƒ is positive and for a concave lens, ƒ is negative, as is clear from fig. 4
The assumptions made in the derivation are:
1. The lens is thin so that distances measured from the poles of its surfaces can be taken as equal to the distances from the optical centering of the lens.
2. The aperture of the lens is small.
3. The object consists only of a point lying on the principle axis of the lens.
4. The incident ray and refracted ray make small angles with the principle axis of the lens.
(a) Convex lens: a convex lens is made up of 2 convex spherical refracting surfaces. The final image is formed after two refractions. In fig. 5 P1, P2 are the poles, C1, C2 are the centres of curvature of two surfaces of a thin convex lens XY with optical centre at C. let 2 be the refractive index of the material of the lens and 1 be the refractive index of the rarer medium around the lens.
Consider a point object O lying on the principle axis of the lens. A ray of light starting from O and incident normally on the surface XP1Y along OP1 passes straight. Another ray incident of light starting from O and incident normally on the surface XP1Y along OP1 passes straight. Another ray incident on XP1Y along OA is refracted along AB. If the lens material were continuous and there were no boundary/second surface XP2Y of the lens, the refracted ray AB would go straight meeting the first refracted ray at I1. Therefore, I1 would have been a real image of O formed after refraction at XP1Y.