A thin lens is nothing but such lenses whose thickness is negligible when compared to their radii of curvature. To gain a better insight into thin lens, refer to this diagram below
Before understanding concave and convex lens formula, take a look at Figure 1.0. Here, thickness (t) is much smaller than the two radii of curvature R1 and R2.
For such a lens, focal length, image distance and object distance are interconnected. One can establish this connection, by the following formula –
1/f = 1/v + 1/u
In this equation, f is the focal length of the lens, while v refers to the distance of the formed image from the lens’ optical centre. Lastly, u is the distance between an object and this lens’ optical centre. This is the lens equation for convex lenses.
To derive a thin lens formula, you must first understand that lenses can be of two types – converging and diverging.
Converging – These are lenses where light rays parallel to the optic axis pass through and converge together at a common point behind it. This point is known as the focal point (f) or focus. Refer to Fig 1.1.
Diverging – These lenses perform a contrasting function to that of converging lenses. Here, the rays of light parallel to the optic axis pass through it and diverge. It gives rise to an optical illusion, making it feel as if the lights come from the same source (f) in front of the lens. Refer to Fig 1.2.
Simply knowing the thin lens formula for convex lens is not enough. You must understand the characteristics of a ray of light passing through converging and diverging lenses.
Parallel rays passing through converging lenses will meet at point f on the other side.
Parallel rays entering diverging lenses seem to arise from point f in front of it.
Light rays passing through the centre of converging or diverging lenses do not change their directions.
Light rays entering a converging lens through its focal point will always exit parallel to its axis.
A light ray heading towards the focal point on the other side of a diverging lens will also come out parallel to its axis.
Focal length is negative for a concave or diverging lens. Similarly, image distance is negative when the image is formed on the side where the object is placed. In such an event, the image is virtual. Positive focal length, on the other hand, denotes a converging or convex lens.
Multiple Choice Question
Which of the Following is True?
Lens power is always negative
Lens power is always positive
Power of concave lens is positive
Power of convex lens is positive
Ans. (d) Power of convex lens is positive
Now that you are aware of focal length of convex lens formula, you should assess the combination of thin lenses in contact. If two such lenses are in contact, the formula to determine the combined focal length is,
1/f = 1/f1 + 1/f2
Here, f is the combined focal length, while f1 is the focal length of the first lens and f2 is the focal length of the second lens. Therefore, for n number of lenses, the focal length is
1/f = 1/f1 + 1/f2 + 1/f3…. + 1/fn
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1. What is the Lens Formula for Convex Lens?
Ans. According to the convex lens equation, 1/f = 1/v + 1/u. It relates the focal length of a lens with the distance of an object placed in front of it and the image formed of that object.
2. When is Image Virtual for a Concave Lens?
Ans. The image formed from a concave lens is virtual only when the object and image are on the same side of the lens.
3. When do Combined Lenses Behave as Convex Lenses?
Ans. If the focal length of the second lens is greater than the first lens’ focal length, the resulting combined lens acts as a convex lens.