Questions: Lens Image Formation and Ray Diagrams

Question 1

An object is placed between a converging lens and its focal point (do < f). What kind of image does the lens form?

• A. A real, inverted image on the far side of the lens — converging lenses always form real images
• B. A virtual, upright, magnified image on the same side as the object
• C. No image is formed when the object is inside the focal length
• D. A real, upright image projected onto a screen on the far side

Answer: (B)

When the object is closer than the focal length (do < f), the three principal rays diverge after passing through the lens. Tracing them backward, they appear to originate from a point on the same side as the object — a virtual image that is upright and magnified. This is how a magnifying glass works: the object (text, insect) is held inside the focal length, and the lens produces a larger, virtual, upright image. The common misconception is that converging lenses always form real images; they only do so when do > f.

Question 2

A slide projector uses a converging lens. The film slide must be placed just beyond one focal length from the lens. The resulting image on the screen will be:

• A. Real, upright, and enlarged — the projector magnifies the image to fill the screen
• B. Real, inverted, and enlarged — which is why film must be loaded upside-down
• C. Virtual, upright, and enlarged — virtual images can be projected if the screen is large enough
• D. Real, inverted, and diminished — the screen is far away, so the image shrinks

Answer: (B)

When do is just slightly greater than f, the thin lens equation gives a very large di. Magnification m = −di/do is large in magnitude and negative — large because di >> do, and negative because the image is inverted. The projected image is greatly enlarged and upside-down. This is why film must be loaded inverted: the lens flips it, producing an upright image on the screen. Option A is wrong because converging lenses with do > f always produce inverted (negative m) real images.

Question 3

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

• T. True
• F. False

Answer: False

False. A diverging lens (negative f) always bends rays outward, spreading them apart. The three principal rays always diverge after passing through a diverging lens, regardless of object distance. Tracing them backward, they always appear to converge on the same side as the object — a virtual image. Diverging lenses cannot project images onto screens because they never produce real images. This is why they are used in corrective lenses for nearsightedness rather than as projectors.

Question 4

A negative magnification (m < 0) means the image is inverted and real.

• T. True
• F. False

Answer: True

True. Magnification m = −di/do. For a real image formed by a converging lens (object beyond focal point), di is positive and do is positive, so m = −di/do is negative. A negative m means the image is flipped relative to the object — inverted. Real images are always inverted for single converging lenses with do > f. Virtual images (formed when do < f for converging, or always for diverging) have positive di (measured on the same side as the object by sign convention), giving positive m and an upright image.

Question 5

Why must film in a slide projector be loaded upside-down?

Model answer: Because a converging lens forms a real, inverted image when the object is beyond the focal length. The lens flips the film image both horizontally and vertically. Loading the film upside-down means the lens's inversion cancels out, and the projected image on the screen appears right-side up. If film were loaded right-side up, the projected image would be inverted.

This is a direct consequence of m = −di/do being negative for real images. The lens inverts the image as it projects it. The projector is designed around this: do is set just barely beyond f so that di (the screen distance) is very large, giving high magnification. The −di/do formula tells you the image is inverted — loading film upside-down is the practical correction for this inevitable inversion.