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Two thin convex lenses of focal lengths f, and f2 are separated by a horizontal distance d (where d

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Two thin convex lenses of focal length $$f_{1}$$ and $$f_{2}$$ are separated by a horizontal distance $$d$$ (where $$d<f_1,d<f_2$$) and their centres are displaced by a vertical separation $$\Delta$$. Taking the origin of co-ordinates $$O$$ at the centre of the first lens, the $$x$$ and $$y$$ co-ordinates of the focal point of this lens system for a parallel beam of rays coming from the left, are given by:

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Assertion :Two convex lenses of same material and equal focal length

^{'} f^{'}

from achromatic combination when separated by distance

^{'} f^{'}

. Reason:

\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}}

where

F =

equivalent focal length of lenses having focal lengths

f_{1}

and

f_{2}

separated by a distance

^{'} d^{'}

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Two thin convex lenses of focal lengths

f_{1}

and

f_{2}

are separated by a horizontal distance

d

(where

d > f_{1}, d > f_{2}

), and their centre are displaced by a vertical separation

Δ

as shown in figure. Taking the origin of coordinates,

O

, at the centre of the first lens, the

x

and

y

coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by

View Solution

Two thin convex lenses of focal length

f_{1}

and

f_{2}

are separated by a horizontal distance

d

(where

d < f_{1}, d < f_{2})

and their centers are displaced by a vertical separation

△

as shown in the figure.
Taking the origin of coordinates

O

at the center of the first lens, the

x

and

y

coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by

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Two thin convex lenses of focal length 10 cm and 15 cm are separated by a distance of 10 cm. The focal length of combination is :-

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