9.20: A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.
Hint: Use the lens formula.
Step 1: Find the location of the image and the object.
The image of the object can be located on the screen for two positions of convex lens such that u and v are exchanged. The separation between two positions of the lens is, d= 20 cm
From the figure,
Solving,
Step 2: Find the focal length of the lens.
From the lens formula,
\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\\frac{1}{55}-\frac{1}{-35}=\frac{1}{f}\\ \Rightarrow \frac{1}{f}=\frac{55\times35}{90}\\ \Rightarrow f=21.4 cm\)
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