Question

Formula of focal length in convex lens is.

Answer 1

Hint: To answer this question, we first need to know the general formula of focal length which is equal to ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}+{\displaystyle \frac{1}{u}}$

Complete answer:
Convex lens - The convex lens is a type of lens that converges rays of light that are parallel to its principal axis.
As pe above formula given in the hint ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}+{\displaystyle \frac{1}{u}}$
And for convex lens u is negative i.e. (the distance between the object and the optical center).
Therefore ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}+{\displaystyle \frac{1}{(-u)}}$
Taking the negative sign out of the bracket.
Now ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}$
Taking LCM ,
${\displaystyle \frac{1}{f}}={\displaystyle \frac{u-v}{uv}}$
Taking reciprocal of ($1/f$)
Finally, $f={\displaystyle \frac{u\times v}{u-v}}$
So, the final answer is $f={\displaystyle \frac{u\times v}{u-v}}$.

Note: When the subject is in focus, the focal length of the lens is the distance between the lens and the image sensor, normally expressed in millimetres (e.g., 28 mm, 50 mm, or 100 mm). The minimum and maximum focal lengths of zoom lenses are defined, for example, 18–55 mm.