The graph below shows the variation of image distance (v) with the object distance (u) when an object is kept in front of a lens. Identify the type of lens used.
Show Hint
Remember the key difference from graphs: A convex lens can form real images (\(v>0\)), while a concave lens always forms virtual images (\(v<0\)) for real objects. A positive v on the graph immediately points to a convex lens.
Step 1: Analyzing the Graph:
The graph shows the relationship between the object distance (\(u\)) and the image distance (\(v\)).
- Object distance (\(u\)) is plotted on the negative X-axis, which is consistent with the sign convention that real objects have a negative object distance.
- Image distance (\(v\)) is plotted on the positive Y-axis. A positive image distance signifies that a real image is formed.
- As the magnitude of the object distance \(|u|\) decreases (i.e., the object moves closer to the lens), the image distance \(v\) increases. Step 2: Relating Graph to Lens Properties:
- A lens that forms a real image for a real object must be a converging lens. A concave (diverging) lens always forms a virtual image for a real object, for which \(v\) would be negative.
- The behavior shown in the graph (real image formation, with \(v\) increasing as \(u\) decreases towards the focal point) is the characteristic property of a convex lens. Step 3: Final Answer:
Since the lens forms a real image (\(v>0\)) for a real object (\(u<0\)), the lens used is a convex lens.
