Convex lenses can also be known as converging lenses since the rays converge after falling on the convex lens while the concave lens is known as diverging lenses as the rays diverge after falling on the concave lens. Images formed by these convex lenses can be real or virtual depending on their position from the lens and can have a different size too. The image distance can be calculated with the knowledge of object distance and focal length with the help of the lens formula.
In optics, the relationship between the distance of an object (o), the distance of an image (i), and the focal length (f) of the lens are given by the formula which is known as the Lens formula. Lens formula is applicable for concave as well as convex lenses. These lenses have negligible thickness. Lens equation or lens formula is an equation that relates the focal length, image distance, and object distance for a spherical mirror. It is given as,
Lens Formula - 1/u + 1/v = 1/f
where.
v = Distance of the image from the lens.
u = Distance of the object from the lens.
f = Focal length of the lens.
This lens formula is applicable to all situations and with appropriate sign conventions. This lens formula is applicable to both the concave lens and convex lens. If the equation shows a negative (-ve) image distance, then the image is a virtual image on the same side of the lens as the object. If this equation shows a negative (-ve) focal length, then the lens is a diverging lens rather than the converging lens. This equation is used to find image distance for either real images or virtual images.
The Power of the Lens
The Power of the Lens is the level at which the Lens meets or separates the light source from it. Now, this combination or separation will depend on how much the Lens is bent. We know that the bending of the Lens causes the Length of the focus. Therefore, the strength of the Lens depends on its Focal Length. A high-angle Lens will have a shorter Focal Length and also means it will have a higher concentration or light separation. Similarly, a slightly curved Lens will have more focus Length and means that it will have less compaction or separation to provide light. Therefore, the Power of the Lens is proportional to the Focal Length of the Lens.
How is the Power of the Lens Affected by its Curvature?
The answer to this question is similar to the one described in terms of Power Dependency. The Power of the Lens is the level at which the Lens meets or separates the light source from it. Now, this combination or separation will depend on how much the Lens is curved. A highly curved Lens means that it will have a high angle of separation or separation to give light to the event. Similarly, a slightly curved Lens means that it will have little or no contact to give light. In this way, the Power of the Lens depends on the angle of the Lens.
Why Multiply by 100 when we Change the Lens Power to focus Length?
The Lens Power of the Length focused on f is defined as 1 / f, where f is expressed in meters. The Power unit is the Diopter (D).
Example: - let us assume that the Length of the Convex Focal Lens is 40 cm.
Then Power = 100/40 = +2.5 D
We multiply 1/40 by 100 in the Example above, because we change the Length of the focus applied to the denominator from centimetres to meters.
Describe the Lens Diopter by an Optician:
A Diopter is a unit used to express the magnification of circular Lenses.
Diopter corresponds to the Focal Length when the Focal Length is defined by the meter.
A good mark is used for Power to change the Lens or Convex Lens.
The negative sign is used for the deviation of the Lens or Concave Lens
Assumptions Related to Lens Formula
The Lens is thin.
The Lens has a small aperture.
The object is lying next to the principal axis.
Incident rays create small angles with the Lens surface or principal axis.
Solved Examples
Example 1: What image is produced by placing an object 6 cm away from a convex lens of focal length equal to 3 cm?
Solution: The question states that u = 6 cm and f = 3 cm. This can be substituted into the lens formula as given below:
1/u + 1/v = 1/f
Therefore, 1/6 + 1/v = 1/3
1/v = 1/3 - 1/6 = 1/6
So v = 6 cm. From the ray diagram we see that this is an inverted, real image.
