Two thin lenses of focal lengths f1 and f2 are placed in contact with each other. The focal length of the combination is :

Question

Two thin lenses of focal lengths f1 and f2 are placed in contact with each other. The focal length of the combination is : (A)  (f1+f2/2)  (B)  √f1 f2  (C)  (f1f2/f1+f2)  (D)  (f1f2/f1-f2)

Tardigrade Admin · Accepted Answer

When f1 and f2 are focal lengths of lenses combined together, image formation takes place as follows, <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/03b146253cfaf783f069020fd710d9c4-.png" /> From lens formula (1/v')-(1/u)=(1/f1) (1/v)-(1/v prime)=(1/f2) Adding Eqs. (i) and (ii) we get (1/v)-(1/u)=(1/f1)+(1/f2) If this lens is replaced by a single lens, then focal length of combination is (1/F)=(1/f1)+(1/f2)=(1/v)-(1/u) ⇒ F=(f1 f2/f1+f2)

Q. Two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are placed in contact with each other. The focal length of the combination is :

$\frac{f _{1} + f _{2}}{2}$

$f_{1} f_{2}$

$\frac{f _{1} f _{2}}{f _{1} + f _{2}}$

$\frac{f _{1} f _{2}}{f _{1} - f _{2}}$

Q. Two thin lenses of focal lengths f1​ and f2​ are placed in contact with each other. The focal length of the combination is :

2f1​+f2​​

f1​​f2​

f1​+f2​f1​f2​​

f1​−f2​f1​f2​​

Q. Two thin lenses of focal lengths $f_{1}$ and $f_{2}$ are placed in contact with each other. The focal length of the combination is :

$\frac{f _{1} + f _{2}}{2}$

$f_{1} f_{2}$

$\frac{f _{1} f _{2}}{f _{1} + f _{2}}$

$\frac{f _{1} f _{2}}{f _{1} - f _{2}}$