An object is placed to the left of a convex lens, an image is formed to the right of the lens. What is the focal length of this lens?

• A.
• B.
• C.
• D.

Answer: (D)

Verified step by step guidance

1. Identify the given quantities: the object distance \(u = -36\operatorname{cm}\) (negative because the object is to the left of the lens) and the image distance \(v = +20\operatorname{cm}\) (positive because the image is formed to the right of the lens).
2. Recall the lens formula which relates the focal length \(f\), the object distance \(u\), and the image distance \(v\): \[\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\]
3. Substitute the known values of \(u\) and \(v\) into the lens formula: \[\frac{1}{f} = \frac{1}{20} - \frac{1}{-36}\]
4. Simplify the right-hand side by calculating the difference of the reciprocals, keeping track of signs carefully.
5. Finally, take the reciprocal of the result to find the focal length \(f\) of the convex lens.