Question

In which situation, the value of focal lenth of the lens is equal to the value of the image distance ?

Answer 1

Answer:

Since the question asked for value of focal length of lens will be equal to image distance, we can say that the image will be formed at the focal point.

For any lens or mirror , this is possible only in 1 case :

• When the object has been placed at infinity

Paraxial rays coming from object at infinity gets refracted from the lens and meets at the focal point on the principle axis (considering point object).

Mathematically , it can be proved .

$\dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u}$

Cancelling focal length and image distance , we get :

$= > \cancel{ \dfrac{1}{f} } = \cancel{ \dfrac{1}{v}} - \dfrac{1}{u}$

$= > - \dfrac{1}{u} = 0$

$= > u = - \infty$

Answer 2

$\tt{\huge{\orange {Hello!!!!}}} N.m$

QUESTION :

In which situation, the value of focal lenth of the lens is equal to the value of the image distance ?

SOLUTION :

The question states that the focal length of the lens is equal to the object Distance.

Hence :

1 / f = 1 / V

But according to the mirror Formulae,

1 / f = 1 / v - 1 / u

So we can state that

- 1 / u = 0

=> - u = Infinity

=> u = - Infinity.

Hence the object is placed at - infinity...