A converging thin lens of focal length f = 5 cm is placed between an object and

Question

A converging thin lens of focal length f = 5 cm is placed between an object and a screen that are separated by 30 cm. There are two values of the object distance o (distance between the object and the lens) that produce sharp (real) images on the screen. Find these two object distances by using the thin-lens formula 1/o +1/i = 1/f and the condition o + i = 30 cm that constrains the object-to-image distance to be fixed at 30 cm. The shorter of the two object distances is? The longer of the two object distances is?

Explanation / Answer

v+u=30 1/v+1/u=1/30 1/(30-u)+1/u=1/5 30/(30u-u^2)=1/5 u^2-30u+150=0 u=6.33cm,23.66cm

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