Answers · Lenses and images

Lenses and images — return questions key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. OR1 · Return

Model answer. (a) The principal focus is the point on the principal axis where rays parallel to the axis all meet after passing through a converging lens. (b) The lens brings the parallel rays together at its principal focus, so they cross the axis 6.5 cm from the lens. Light carries on in straight lines, so beyond F the rays spread out again, and a screen 13 cm behind the lens, at 2f, shows a blurred patch of light about as wide as the beam was at the lens, not a point. (c) The parallel ray is refracted through F on the far side, so after the lens it falls by the height of the object over one focal length. The ray through the centre goes straight on, and since the tip of the object is directly above the near F, it also falls by the height of the object over one focal length. The two rays leave the lens parallel to each other and never cross, so there is no image at any distance. (d) A converging lens forms a real image only of an object further away than f = 25 cm, and that image is enlarged only while the object is nearer than 2f = 50 cm. So the figure must be between 25 cm and 50 cm from the lens.

A full answer includes

(a) I wrote that it is a point on the principal axis.
(a) I wrote that rays parallel to the axis pass through it after the lens.
(b) I wrote 6.5 cm.
(b) I wrote that the screen shows a blurred patch of light, not a point.
(b) I gave the reason: the rays cross at 6.5 cm and then spread out again.
(c) I wrote that the two rays leave the lens parallel to each other.
(c) I wrote that they never cross.
(c) I wrote that there is no image at any distance.
(d) I wrote further than 25 cm from the lens.
(d) I wrote nearer than 50 cm, which is 2f.
I did not put the figure nearer than 25 cm, where the image is virtual.

Also accept

(a) point where parallel rays meet (b) 6.5 cm; a blurred patch (c) they leave parallel and never cross: no image (d) between 25 cm and 50 cm

Watch for

“The principal focus is the centre of the lens.” — The centre of the lens is where the principal axis crosses it. The principal focus is a focal length away from it.
“A screen 13 cm behind the lens shows nothing, because the light stops at F.” — Light carries on in straight lines: the rays cross at F and spread out again, so the screen shows a blurred patch.
“With the object at F, the image is at F on the far side, where the parallel ray crosses the axis.” — Only one ray crosses the axis there. The two rays from the tip leave the lens parallel to each other, so they never meet.
“The figure must be nearer than 25 cm for an enlarged image.” — Nearer than f, the image is virtual and no screen can show it. A real, enlarged image needs the figure between f and 2f.

2. OR2 · Return

Model answer. (a) A virtual image is formed where diverging rays, extrapolated backwards, seem to come from. No light actually passes through it, so a screen there shows nothing. (b) The coin must be closer to the lens than its principal focus, less than 5.0 cm away, and the eye looks through the lens from the other side, close to it; it sees an upright, enlarged image of the date. (c) Extrapolate both rays backwards with dashed lines; the point where the dashed lines meet, on the object’s side, is the tip of the image. (d) Long sight is corrected with a converging lens, so her reading glasses are converging. A long-sighted eye sees distant things clearly without help: it already brings the rays from the clock together on the retina. The converging lens starts bringing these rays together before they enter the eye, so now they meet too soon, in front of the retina, and the clock looks blurred.

A full answer includes

(a) I wrote that the rays only seem to come from a virtual image.
(a) I wrote that no light passes through the image.
(b) I wrote that the coin is closer to the lens than 5.0 cm.
(b) I wrote that the eye is on the other side of the lens, close to it.
(c) I extrapolated both rays backwards with dashed lines.
(c) I put the tip of the image where the dashed lines meet.
(d) I wrote a converging lens.
(d) I wrote that without glasses her eye brings the rays from the distant clock together on the retina.
(d) I wrote that the converging lens brings these rays together sooner.
(d) I wrote that they then meet in front of the retina.
I did not write that a virtual image cannot be seen.

Also accept

(a) no light passes through it (b) coin inside F, closer than 5.0 cm; eye on the other side (c) where the backward dashed lines meet (d) converging; the rays from the clock now meet in front of the retina

Watch for

“A virtual image cannot be seen.” — It can be seen, by looking into the lens; it cannot be caught on a screen.
“The tip of the image is where the rays cross the axis after the lens.” — Only one ray crosses the axis there. The image is where both rays, traced backwards, meet.
“Reading glasses for long sight have a diverging lens.” — Long sight is corrected with a converging lens: rays from near things would meet behind the retina, so they need bringing together sooner.
“The clock blurs because the glasses make it look bigger.” — Blur is about where the rays meet, not size. The extra bending makes the rays from the clock meet in front of the retina.