Answers · Lenses and images

Lenses and images — final check key

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

1. OK1 · Final check

Model answer. (a) The focal length is the distance from the centre of the lens to its principal focus. (b) The principal axis is the line through the centre of the lens at right angles to it. (c) At half size, F is 6.0 cm from the lens on each side, and the object is 15 cm from the lens and 1.5 cm tall. The ray parallel to the axis is refracted through F on the far side, and the ray through the centre goes straight on. They cross 10 cm from the lens on the paper, 1.0 cm below the axis. Doubled, the image is 20 cm from the lens and 2.0 cm tall. (d) It is real, inverted and diminished: the object is further away than 2f = 24 cm.

Checked automatically

(c) Distance of the image from the lens (real cm): 20 cm (within ±1.5 cm)
- Common wrong answer 10 : That is the distance on your paper. At half size, double it.
- Common wrong answer 12 : That is the principal focus. Find where your two rays cross.
(c) Height of the image (real cm): 2.0 cm (within ±0.3 cm)
- Common wrong answer 1 : That is the height on your paper. At half size, double it.
- Common wrong answer 3 : That is the height of the object. Measure the image, below the axis.

A full answer includes

(a) I wrote: the distance from the centre of the lens to the principal focus.
(b) I wrote: the line through the centre of the lens at 90° to it.
(c) I drew F 6.0 cm from the lens on the paper.
(c) I drew the object 15 cm from the lens on the paper.
(c) I drew the object 1.5 cm tall on the paper.
(c) I drew the parallel ray, then through F on the far side.
(c) I drew the ray through the centre of the lens straight on.
(c) Distance, method: I measured where the rays cross on the paper and doubled it.
(c) Distance, answer: I wrote about 20 cm.
(c) Height, method: I measured the image on the paper and doubled it.
(c) Height, answer: I wrote about 2.0 cm.
(d) I wrote real, inverted and diminished.
I did not give 10 cm or 1.0 cm, the lengths on the paper.

Also accept

(a) lens to F (b) line through the centre at 90° (c) 20 cm, 2.0 cm (d) real, inverted, diminished

Watch for

“The focal length is the distance from the lens to the image.” — Only the image of a very distant object is at the principal focus. The focal length is the distance from the centre of the lens to F.
“The image is 10 cm from the lens.” — That is the distance on the paper. At half size, double it: 20 cm.
“The image is enlarged, because the object is further than F.” — Further than f makes the image real. The object is also further than 2f, so the image is diminished.

2. OK2 · Final check

Model answer. (a) The converging lens brings the parallel beam together at its principal focus, 15 cm behind it, so the screen shows a small bright spot. The diverging lens spreads the beam out, as if from its principal focus 15 cm in front of it, so the screen shows a round patch of light wider than the lens and no sharp spot. (b) No screen could show it. The rays from each point of the print are already spreading out, and the diverging lens spreads them out even more, so after the lens they never meet. They only seem to come from an upright, smaller image on the page’s side of the lens: a virtual image, where no light actually passes. (c) Beyond 9.0 cm the screw is further than the principal focus. The rays from it then leave the lens coming together, towards a real, inverted image, so the upright, magnified view blurs and then turns upside down. (d) Mark F 9.0 cm from the lens on each side and draw the screw 3.0 cm from the lens, 0.8 cm tall. From its tip, the ray parallel to the axis is refracted through F on the far side, and the ray through the centre goes straight on. They spread apart, so extrapolate both backwards: the dashed lines meet 4.5 cm from the lens on the screw’s side, 1.2 cm above the axis. The image is 4.5 cm from the lens and 1.2 cm tall. (e) A short-sighted eye brings the rays from a distant object together too soon, in front of the retina. A diverging lens spreads them out a little before they enter the eye, so they meet on the retina.

Checked automatically

(d) Supplement: Distance of the image from the lens: 4.5 cm (within ±0.5 cm)
- Common wrong answer 9 : That is the focal length. Find where the dashed lines meet.
- Common wrong answer 3 : That is where the screw is. The image is further from the lens than the screw.
(d) Supplement: Height of the image: 1.2 cm (within ±0.2 cm)
- Common wrong answer 0.8 : That is the height of the screw. Measure the image, where the dashed lines meet.

A full answer includes

(a) Converging lens: I wrote a small bright spot.
(a) Converging lens: I wrote that the rays meet at the principal focus, on the screen.
(a) Diverging lens: I wrote a patch of light wider than the lens.
(a) Diverging lens: I wrote that there is no sharp spot anywhere.
(b) I wrote that a screen could not show it.
(b) I wrote that the lens spreads the rays from the print out even more.
(b) I wrote that the rays never meet after the lens.
(b) I wrote that the image is virtual.
(c) I wrote that the screw would then be further than the principal focus.
(c) I wrote that the rays would then leave the lens coming together.
(c) I wrote that the view blurs and then turns upside down.
(d) Distance, method: I measured from the lens to where the dashed lines meet.
(d) Distance, answer: I wrote about 4.5 cm.
(d) Side: I put the image on the same side of the lens as the screw.
(d) Height, method: I measured from the axis up to where the dashed lines meet.
(d) Height, answer: I wrote about 1.2 cm.
(e) I wrote that the eye brings rays from distant objects together in front of the retina.
(e) I wrote that the diverging lens spreads the rays out a little first.
(e) I wrote that the rays then meet on the retina.
I did not write that the diverging lens gives a bright spot behind it.

Also accept

(a) a bright spot; a patch wider than the lens (b) no: the lens spreads the rays more, they never meet, the image is virtual (c) beyond F the rays come together: the view blurs and turns over (d) 4.5 cm, 1.2 cm (e) rays meet in front of the retina; the diverging lens moves them onto it

Watch for

“The diverging lens also gives a bright spot, 15 cm behind it.” — Its rays never meet behind it. Its principal focus is in front, where the rays only seem to come from.
“A screen above the lens could show the smaller print, because a small image is easy to catch.” — Size does not decide. The rays leaving a diverging lens are spreading out, so they never meet, and no screen can show the image.
“The image is 9.0 cm from the lens, at F.” — That is the focal length. Find where the two dashed lines meet.