Question

The focal length of a convex lens is $20\text{ cm}$. An object is placed at $40\text{ cm}$ from the lens. The image formed will be:

• A. Virtual and erect
• B. Real and inverted
• C. Virtual and inverted
• D. Real and erect

Hint:

Whenever an object is placed at $2F$ ($u = 2f = 40\text{ cm}$) for a convex lens, the image is formed on the other side at $2F$. Like all real images formed by a single lens, it is Real and Inverted.

Answer 1

The Correct Option is B

Concept: Ray optics principles for a converging (convex) lens establish predictable image characteristics based on where the object is located relative to the lens's focal point ($F$) and center of curvature ($2F$).

Step 1: Analyze the object placement relative to the focal metrics.
Let's look at the given values from the problem:
• Focal length ($f$) = $+20\text{ cm}$
• Center of curvature distance ($2f$) = $2 \times 20\text{ cm} = 40\text{ cm}$
• Object distance ($u$) = $-40\text{ cm}$ This shows that the object is placed exactly at the center of curvature ($2F$) on the left side of the convex lens.

Step 2: Apply the lens principles to determine image traits.
When an object is located exactly at $2F_1$ for a convex lens:
• The image is formed on the opposite side of the lens at exactly $2F_2$ ($v = +40\text{ cm}$).
• The image is the exact same size as the object ($m = -1$).
• The light rays physically converge at that point, making the image Real and Inverted.