Question

a rubber ducky is placed 20 cm from a thin convex lens with a focal length of 15 cm. which statement correctly describes the nature and position of the image formed of the rubber ducky? a real and upright on the side of the lens opposite the rubber ducky. b real and inverted on the side of the lens opposite the rubber ducky. c imaginary and upright on the side of the lens opposite the rubber ducky. d imaginary and inverted on the same side of the lens as the rubber ducky.

Explanation:

Step1: Recall Lens Formula

The lens formula is $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$, where $f$ is the focal length, $u$ is the object distance, and $v$ is the image distance. For a convex lens, $f$ is positive. Here, $u = 20\ \text{cm}$ (object distance, positive as per sign convention), $f = 15\ \text{cm}$.

Step2: Calculate Image Distance

Substitute values into the formula: $\frac{1}{15} = \frac{1}{20} + \frac{1}{v}$. Solve for $\frac{1}{v}$: $\frac{1}{v} = \frac{1}{15} - \frac{1}{20} = \frac{4 - 3}{60} = \frac{1}{60}$. So, $v = 60\ \text{cm}$. Positive $v$ means image is real and on the opposite side of the lens from the object.

Step3: Determine Image Nature

For a convex lens, when the object is between $f$ and $2f$ (here, $f = 15$, $2f = 30$; $u = 20$ is between them), the image formed is real, inverted, and magnified. So the image is real, inverted, and on the opposite side.

Answer:

B. Real and inverted on the side of the lens opposite the rubber ducky.