A converging lens having magnitude of focal length as f1 is kept coaxially in contact with a diverging lens having magnitude of focal length as f2 . The focal length of the combination would be:

Question

A converging lens having magnitude of focal length as f1 is kept coaxially in contact with a diverging lens having magnitude of focal length as f2 . The focal length of the combination would be: (A) (f1 f2/f1 - f2) (B) (f1 + f2/f1 f2) (C) (f1 - f2/f1 f2) (D) (f1 f2/f1 + f2)

Tardigrade Admin · Accepted Answer

We have to consider sign convention as only magnitude of focal length is given.
If

f_{1}

is focal length of convex (converging) lens and

f_{2}

is focal length of concave (diverging) lens. Then their equivalent focal length F would be

\frac{1}{F} = \frac{1}{f _{1}} + \frac{1}{- f _{2}} = \frac{f _{2} - f _{1}}{f _{1} f _{2}} [∵ \frac{1}{F} = \frac{1}{f _{1}} + \frac{1}{f _{2}}] ∴ F = \frac{f _{1} f _{2}}{f _{2} - f _{1}}

Q. A converging lens having magnitude of focal length as $f_{1}$ is kept coaxially in contact with a diverging lens having magnitude of focal length as $f_{2}$ . The focal length of the combination would be:

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

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

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

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

Q. A converging lens having magnitude of focal length as f1​ is kept coaxially in contact with a diverging lens having magnitude of focal length as f2​ . The focal length of the combination would be:

f1​−f2​f1​f2​​

f1​f2​f1​+f2​​

f1​f2​f1​−f2​​

f1​+f2​f1​f2​​

Q. A converging lens having magnitude of focal length as $f_{1}$ is kept coaxially in contact with a diverging lens having magnitude of focal length as $f_{2}$ . The focal length of the combination would be:

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

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

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

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