Numerical

**Solve Numerical example.**

A point object is kept 10 cm away from one of the surfaces of a thick double convex lens of refractive index 1.5 and radii of curvature 10 cm and 8 cm. Central thickness of the lens is 2 cm. Determine location of the final image considering paraxial rays only.

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#### Solution

Given that, R_{1} = 10 cm, R_{2 }= – 8 cm, u = – 10 cm and n = 1.5

From lens maker’s equation,

`1/"f"=("n"-1)(1/"R"_1-1/"R"_2)`

∴ `1/"f"=(1.5-1)(1/10-1/-8)`

= `0.5xx9/40=9/80`

∴ f = `80/9` cm

Now,

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

∴ `1/"v"=1/"f"+1/"u"=9/80+1/-10=1/80`

∴ v = 80 cm

The final location of the image will be at **80 cm** from the lens.

Concept: Refraction at a Spherical Surface and Lenses

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