Question

Two thin convex lenses having focal lengths 5cm and 2cm are coaxial separated by a distance of
3cm. Find the equivalent focal length?
(A) 3.75 cm
(B) 2.5 cm
(C)-1.5 cm
(D) 1.5 cm​

Answer 1

Answer:

answer is 3.75 cm

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Answer 2

Given :

Focal length of Lens 1 ($F_{1}$) = 5 cm

Focal length of Lens 2 ($F_{2}$) = 2 cm

The distance between the lenses (d) = 3 cm

To Find :

Equivalent Focal Length ($F_{eq}$)

Solution :

We know, when the two lenses are placed co-axially at a distance 'd', the expression for equivalent focal length is given as -

    $\frac{1}{F_{eq} } = \frac{1}{F_{1} } + \frac{1}{F_{2} } - \frac{d}{F_{1}F_{2} }$  

(where, $F_{1}$ = Focal length of Lens 1 ; $F_{2}$ = Focal length of Lens 2 ; d =  distance between the lenses ; $F_{eq}$ = Equivalent Focal Length)

or, $\frac{1}{F_{eq} }$  = $\frac{1}{5} + \frac{1}{2} -\frac{3}{5 * 2}$

or, $\frac{1}{F_{eq} }$  = $\frac{1}{5} + \frac{1}{2} -\frac{3}{10}$

or, $\frac{1}{F_{eq} }$  = $\frac{2 + 5 - 3}{10}$

or, $\frac{1}{F_{eq} }$  = $\frac{7 - 3}{10}$

or, $\frac{1}{F_{eq} }$  = $\frac{4}{10}$

∴  $F_{eq}$   = $\frac{10}{4}$ = 2.5 cm

∴ The equivalent focal length is 2.5 cm.