Find focal length

Question

A lighted candle is placed 38 cm in front of a diverging lens. The light passes through the diverging lens and on to a converging lens of focal length 10 cm that is 5 cm from the diverging lens. The final image is real, inverted, and 19 cm beyond the converging lens. Find the focal length of the diverging lens.

Answer 1

Hello Vishal,

 

This solution uses the convention REAL is positive(+) and Virtual is negative (-)

 

For the converging lens we have a f = 10 cm, and v = 19 cm, u =?

 

Using (1/v) + (1/u) = (1/f) we will get u = (190/9).

 

Thus for the converging lens there is a real object at a distance of (190/9) cm.

 

A real object is a source of diverging rays, just like a Virtual Image.

 

Thus the diverging lens forms a Virtual image of the lens at a distance of (190/9) - 5 cm = (145/9) cm on the same side as the object. 

 

Using (1/v) + (1/u) = (1/f) we will get f = 28 cm (approx.) using u = 38 cm , v= - (145/9).

 

wish you the best,

 

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Pradip M