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Answer: 24cm

Explanation:

Let  the representation of rays after reflecting from  convex lens.  Here red lines shows IMAGINARY lines.

In this case,

Distance of object from the lens (u) = -20 CM.

Distance of of IMAGE from the lens (v) = ?

Focus of this lens (F) = 40  cm.

For convex lens:-

By using lens formula,

1/f = 1/v - 1/u

1/40 = 1/v + 1/20

1/40 - 1/20 = 1/v

1/40 - 2/40 = 1/v

-1/40 = 1/v

v = -40 cm.

Here NEGATIVE sings show that image formed is 40 cm far from the optic centre in the opposite direction of ray or left side of lens(as per given arrangement). Basically Image is imaginary.

Now, This imaginary image will work as  object for the concave lens.

For concave lens:-

u = -(40 + 20)  = -60 cm

v = ?

f = -40 cm

By using lens formula,

1/f = 1/v - 1/u

-1/40 = 1/v + 1/60

-1/40 - 1/60 = 1/v

-3/120 - 2/160 = 1/v

-5/120 = 1/v

v = -24 cm  


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