Questions: Thin Lenses: Converging and Diverging

Question 1

A movie projector needs to cast a large, sharp image onto a screen several meters away. Which lens configuration achieves this?

• A. A diverging lens with the film slide placed inside the focal length
• B. A converging lens with the film slide placed between f and 2f
• C. A converging lens with the film slide placed beyond 2f
• D. Either lens type can project an image with the right screen distance

Answer: (B)

A projector needs a real, inverted, magnified image — which requires a converging lens with the object (slide) placed between f and 2f. In that configuration, the image forms beyond 2f on the far side, is real (it can be projected onto a screen), inverted, and magnified. If the slide were beyond 2f, the image would be real and inverted but reduced. Diverging lenses can never project a real image under any circumstances.

Question 2

An object is placed 8 cm in front of a converging lens with focal length 12 cm. Where does the image form and what are its properties?

• A. Beyond the lens — real, inverted, and reduced
• B. Beyond the lens — real, inverted, and magnified
• C. On the same side as the object — virtual, upright, and magnified
• D. At the focal point on the far side of the lens

Answer: (C)

The object is at 8 cm, inside the focal length of 12 cm (d_o < f). When an object is inside f for a converging lens, the refracted rays still diverge after the lens — they cannot converge to a real image on the far side. Their backward extensions meet on the same side as the object, producing a virtual, upright, magnified image. This is exactly how a magnifying glass works.

Question 3

A diverging lens can form a real image if the object is placed far enough away from the lens.

• T. True
• F. False

Answer: False

Diverging lenses always produce virtual images — this is a firm rule with no exceptions based on object distance. A diverging lens spreads rays outward; no matter how far the object, parallel incoming rays are still bent to diverge, appearing to come from a virtual focal point on the incoming side. Real images require rays that actually converge on the far side, which a diverging lens cannot produce regardless of object placement.

Question 4

When an object is placed between the focal point and a converging lens, the lens acts as a magnifying glass, producing a virtual, upright, enlarged image.

• T. True
• F. False

Answer: True

With the object inside the focal length (d_o < f), a converging lens cannot converge the rays to a point on the far side — they still diverge after refraction. Looking through the lens from the far side, you trace these diverging rays backward and find they appear to originate from a point on the same side as the object — further away and larger. This virtual, upright, magnified image is the defining behavior of a magnifying glass.

Question 5

Explain why the character of the image formed by a converging lens changes so dramatically when the object crosses the focal point.

Model answer: When the object is outside the focal length, rays from each object point arrive at the lens at angles that allow the lens's bending to converge them to a real meeting point on the far side. When the object moves inside f, those rays arrive at steeper angles — the lens still bends them, but not enough to make them cross on the far side. They continue to diverge after the lens, and only their backward extensions appear to converge on the same side as the object. The focal point is exactly the transition: at d_o = f, the emerging rays are parallel and converge 'at infinity.'

The focal point marks the boundary between the converging and diverging output regimes. Beyond f, emerging rays converge (real image on the far side). Inside f, they diverge (virtual image traced back to the near side). At exactly f, they emerge parallel — the image distance becomes infinite. Understanding this transition is key to predicting image type and location for any object distance.