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Date	November 2020	Marks available	2	Reference code	20N.3.SL.TZ0.11
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Calculate	Question number	11	Adapted from	N/A

Question

A beam of monochromatic light from infinity is incident on a converging lens A. The diagram shows three wavefronts of the light and the focal point $f$ $f$ of the lens.

Draw on the diagram the three wavefronts after they have passed through the lens.

[2]

a.

Lens A has a focal length of $4.00 cm$ $4.00 cm$ . An object is placed $4.50 cm$ $4.50 cm$ to the left of A. Show by calculation that a screen should be placed about $0.4 m$ $0.4 m$ from A to display a focused image.

[2]

b.

The screen is removed and the image is used as the object for a second diverging lens B, to form a final image. Lens B has a focal length of $2.00 cm$ $2.00 cm$ and the final real image is $8.00 cm$ $8.00 cm$ from the lens. Calculate the distance between lens A and lens B.

[3]

c.

Calculate the total magnification of the object by the lens combination.

[2]

d.

Markscheme

wavefront separation identical and equal to separation before the lens ✓

wavefronts converging, approximately centered on $f$ $f$ ✓

By eye.

Dotted construction lines are not required, allow wavefronts to extend beyond or be inside the dotted lines here.

Allow [1 max] if only two wavefronts drawn.

a.

$\frac{1}{v} = \frac{1}{4.00} - \frac{1}{4.50}$ $\frac{1}{v} = \frac{1}{4.00} - \frac{1}{4.50}$ ✓

$v = 36.0 « cm »$ ✓

b.

$A : \frac{1}{- 2.0} = \frac{1}{8} + \frac{1}{u}$ ✓

$u = - 1.6 « cm »$ ✓

distance necessary = $« 36.0 - 1.6 = » 34.4 « cm »$ ✓

Allow [2 max] for ECF for no negative in MP1. Gives $u = 2.7$ and distance of $38.7 « cm »$

Allow ECF from (b) in MP3.EG use of $0.4 m / 40 c m$ .

c.

« $m = - \frac{i}{o} = \frac{- 36}{4.5}$ for A or $\frac{- 8}{- 1.6}$ for B»

$m_{A} = « - » 8$ OR $m_{B} = « + » 5$ ✓

total magnification $= « - » 40$ ✓

Allow [2] marks for a bald correct answer

Allow ECF from (b) and (c).

Eg if $u = 2.7 c m$ in (c) then $m_{B} = 3$ and total $m = 24$

d.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.

Syllabus sections

Option C: Imaging » Option C: Imaging (Core topics) » C.1 – Introduction to imaging

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Option C: Imaging » Option C: Imaging (Core topics)

Option C: Imaging