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Numerical

**Answer the following question.**

Three lenses of focal length +10 cm, —10 cm and +30 cm are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.

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#### Solution

`1/v - 1/u = 1/f`

`u = -30 cm`

`f = +10 cm`

`1/nu = 1/f + 1/u`

`1/nu_1 = 1/10 - 1/30`

⇒ `1/nu_1 = (3 - 1)/30 = 2/30`

`nu_1 = 15` cm

`u = +10 cm`

`f = -10 cm`

`1/nu_2 = 1/f + 1/u = 1/10 - 1/10`

`nu_2 = ∞`

For third lens object is at infinity hence image is formed at focus final image at a distance of 30 cm.

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