What is the Lens formula?
The lens formula can be described as the relationship between the focal length, the distance of an object, and the lens’ image. The lens formula is appropriate for both convex and concave lenses. The thickness of the lenses is negligible. The lens formula is as follows:
1/v – 1/v = 1/f
Here, v is the distance of an image
f is the focal length
u is the distance of an object.
Derivation of lens formula
There are two types of lens, concave and convex lens.
Derivation on the convex lens:
Let us consider a convex lens having an optical center as O, F being the principal focus.
So, A’B’/AB = OB’/OB
The triangles ΔABO and ΔA’B’O are similar to each other
In the same way, ΔA’B’F and ΔOCF are similar to each other
So, A’B’/OC = FB’/OF
Now, OC = AB
So, A’B’/AB = FB’/OF
From the above equations, we can get,
OB’/OB = FB’/OF = (OB’ – OF) / OF
Using sign convention,
OB = -u, OB’ = v and OF = f
We get, v/-u = (v-f) / f
Which means vf = -uv + uf
Or, uv = uf – vf
Hence, 1/f = 1/v + 1/u
Derivation on the concave lens:
Let us assume that the AB is perpendicular to the principal axis and the distance is f of the convex lens. Here, we can assume,
OF1 as focal length
OA as the distance of the object
OA as image distance,
And ΔOAB and ΔOA’B’ are equal to each other
Angle BAO = angle B’A’O = 90°, and O is common in both the angles.
So, angle AOB = angle A’OB’
Now, angle. ABO and A’B’O are equal
And, A’B’/AB = OA’/OA
So, A’B’/OC = A’F1/ OF1
Now from the above equations, we get,
OA’ / OA = (OF1 – OA’) OF1
-v / -u = (-f - - v) / -f
V / u = (-f + v) / -f
-vf = -uf +uv
Let us now divide the above equation by uvf
-1/ u = -1/v + 1/f
Hence, 1/f = 1/v – 1/u
And this is the formula of the concave lens.
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Derivation of lens formula for class 12
As per the new pattern 2021, the chapter ' Optics' holds a significant weightage of 7 marks. These 7 marks include 2 questions in total, one short question of 2 marks, and one long question of 5 marks.
Example 1) Illustrate the lens formula for the convex lens.
Answer – The lens formula for convex lens is 1/f = 1/v + 1/u
Example 2) Write the sign of v in a concave lens.
Answer – The sign of v in the concave lens is positive due to the incident rays.
Example 3) Write the name of the lens used in the torchlight.
Answer – Torch lights use a diverging lens, also known as a concave lens to make the parallel light spread out evenly.
FAQs on Derivation of lens formula
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