name: p6 lenses · a student investigated how the magnification produced by a convex lens varies...

P6 LENSESQuestion Practice

Name: ________________________

Class: ________________________

Date: ________________________

Time: 98 minutes

Marks: 97 marks

Comments: GCSE PHYSICS ONLY

of 38Immanuel+College

A student investigated how the magnification produced by a convex lens varies with the distance(d) between the object and the lens.

The student used the apparatus shown in Figure 1.

Figure 1

(a) The student measured the magnification produced by the lens by measuring the imageheight in centimetres.

Explain why the image height in centimetres was the same as the magnification.

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(2)

1


(b) The data recorded by the student is given in Table 1.

Table 1

Distance between theobject and the lens in cm

Magnification

25 4.0

30 2.0

40 1.0

50 0.7

60 0.5

It would be difficult to obtain accurate magnification values for distances greater than 60cm.

Suggest one change that could be made so that accurate magnification values could beobtained for distances greater than 60 cm.

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(1)


(c) The graph in Figure 2 is incomplete.

Figure 2

Complete the graph in Figure 2 by plotting the missing data and then drawing a line of bestfit.

(2)

(d) How many times bigger is the image when the object is 35 cm from the lens compared towhen the object is 55 cm from the lens?

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(2)


(e) During the investigation the student also measured the distance between the lens and theimage.

Table 2 gives both of the distances measured and the magnification.

Table 2

Distance between the lensand the image in cm

Distance between the lensand the object in cm

Magnification

100 25 4.0

60 30 2.0

40 40 1.0

33 50 0.7

30 60 0.5

Consider the data in Table 2.

Give a second way that the student could have determined the magnification of the object.

Justify your answer with a calculation.

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(2)

(Total 9 marks)


(a) Figure 1 shows a ray of light entering a glass block.

2

(i) The angle of incidence in Figure 1 is labelled with the letter i.

On Figure 1, use the letter r to label the angle of refraction.

(1)

(ii) Figure 2 shows the protractor used to measure angles i and r.

What is the resolution of the protractor?

Tick ( ) one box.

1 degree 5 degrees 10 degrees

(1)


(iii) The table shows calculated values for angle i and angle r from an investigation.

Calculated values

sin i = 0.80

sin r = 0.50

Use the values from the table to calculate the refractive index of the glass.

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Refractive index = _________________

(2)

(b) The diagrams below show a ray of light moving through glass.

Which diagram correctly shows what happens when the ray of light strikes the surface ofthe glass at the critical angle?

Tick ( ) one box.

(1)


(c) A concave (diverging) lens is fitted into a door to make a security spyhole.

Figure 3 shows how this lens produces an image.

(i) State one word to describe the nature of the image in Figure 3.

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(1)

(ii) Use data from Figure 3 to calculate the magnification of the image.

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Magnification = __________________________

(2)


(iii) What is another use for a concave lens?

Tick ( ) one box.

A magnifying glass

Correcting short sight

To focus an image in a camera

(1)

(Total 9 marks)

A student investigates how the magnification of an object changes at different distances from aconverging lens.The diagram shows an object at distance d from a converging lens.

3


(a) (i) The height of the object and the height of its image are drawn to scale.

Use the equation in the box to calculate the magnification produced by the lensshown in the diagram.

magnification =

Show clearly how you work out your answer.

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Magnification = _________________________

(2)

(ii) The points F are at equal distances on either side of the centre of the lens.

State the name of these points.

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(1)

(iii) Explain how you can tell, from the diagram, that the image is virtual.

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(1)


(b) The student now uses a different converging lens. He places the object between the lensand the point F on the left.

The table shows the set of results that he gets for the distance d and for the magnificationproduced.

Distance dmeasured in cm

Magnification

5 1.2

10 1.5

15 2.0

20 3.0

25 6.0

His friend looks at the table and observes that when the distance doubles from 10 cm to 20cm, the magnification doubles from 1.5 to 3.0.

His friend’s conclusion is that:

The magnification is directly proportional to the distance of the object from the lens.

His friend’s observation is correct.

His friend’s conclusion is wrong.

(i) Explain using data from the table why his friend’s conclusion is wrong.

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(2)

(ii) Write a correct conclusion.

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(1)


(iii) The maximum range of measurements for d is from the centre of the lens to F on theleft.

The student cannot make a correct conclusion outside this range.

Explain why.

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(1)

(Total 8 marks)

The diagram shows a lens, the position of an object and the position of the image of the object.

4

(a) What type of lens is shown?

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(1)

(b) What is the name of the points, F, shown each side of the lens?

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(1)

(c) (i) The image is real and can be put on a screen.

How can you tell from the diagram that the image is real?

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(1)

(ii) Draw a ring around a word in the box which describes the image produced by thelens.

inverted larger upright

(1)


(d) A student investigates the relationship between the distance from the object to the lens andthe magnification produced by the lens.The student’s results are given in the table.The student did not repeat any measurements.

Distancein millimetres

Height of objectin millimetres

Height of imagein millimetres

Magnificationproduced

40 20 58 2.9

50 20 30 1.5

60 20 20 1.0

70 20 14 0.7

80 20 12 0.6

90 20 10 0.5

The student plots the points for a graph of magnification produced against distance.

(i) Draw a line of best fit for these points.

(1)


(ii) Complete the following sentence by drawing a ring around the correct word in thebox.

A line graph has been drawn because both variables are

categoric.

described as being continuous.

discrete.

(1)

(iii) Describe the relationship between magnification produced and distance.

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(2)

(Total 8 marks)

A student investigates how the magnification of an object changes at different distances from aconverging lens.

The diagram shows an object at distance d from a converging lens.

5


(a) (i) The height of the object and the height of its image are drawn to scale.

Use the equation in the box to calculate the magnification produced by the lensshown in the diagram.


______________________________________________________________

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Magnification = ______________________________

(2)

(ii) The points F are at equal distances on either side of the centre of the lens.

State the name of these points.

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(1)

(iii) Explain how you can tell, from the diagram, that the image is virtual.

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(1)


(b) The student now uses a different converging lens. He places the object between the lensand point F on the left.

The table shows the set of results that he gets for the distance d and for the magnificationproduced.

Distance dmeasured in cm

Magnification

5 1.2

10 1.5

15 2.0

20 3.0

25 6.0

His friend looks at the table and observes that when the distance doubles from 10 cm to 20cm, the magnification doubles from 1.5 to 3.0.

His friend’s conclusion is that:

The magnification is directly proportional to the distance of the object from thelens.

His friend’s observation is correct but his friend’s conclusion is not correct.

(i) Explain, with an example, why his friend’s conclusion is not correct.

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(2)

(ii) Write a correct conclusion.

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(1)


(iii) The maximum range of measurements for d is from the centre of the lens to F on theleft.

The student cannot make a correct conclusion outside this range.

Explain why.

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(1)

(Total 8 marks)

(a) The diagrams below show rays of light striking a mirror and a perspex block.

6

Complete the paths of the three rays of light on the diagrams to show the rays leaving themirror and the perspex block.

(4)

(b) The diagram below shows a beam of light striking a perspex block.

(i) Continue the paths of the rays AB and CD inside the perspex block.

(ii) Draw the wavefronts of the beam of light in the perspex.


(iii) Explain why the beam behaves in the way you have shown.

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(7)

(c) The diagram below shows a ray of light striking a perspex-air surface from inside theperspex. The critical angle is 45º.

Draw the path of the ray after it reaches the perspex-air boundary.

(2)

(Total 13 marks)

(a) A light bulb is placed between a convex lens and the principle focus of this lens, at positionN shown in Figure 1. The light bulb is then moved to position M, a large distance from thelens.

Figure 1

Describe how the nature of the image formed changes as the light bulb is moved fromposition N to position M.

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(3)

7


(b) An object, O, is very near to a convex lens, as shown in Figure 2.

Complete Figure 2 to show how rays of light from the object form an image.

Figure 2

(3)


(c) The object distance is the distance from an object to the lens. The image distance is thedistance from the lens to the image.

Figure 3 shows how the image distance changes with the object distance, for twoidentically shaped convex lenses, A and B. Each lens is made from a different type ofglass.

Figure 3

(i) When the object distance is 4 cm, the image distance for lens A is longer than forlens B.

State why.

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(1)


(ii) When the object is moved between lens B and the principal focus, the image sizechanges. The table shows the magnification produced by lens B for different objectdistances.

Object distance in cm Magnification

0.0 1

5.0 2

6.7 3

7.5 4

8.0 5

Using information from Figure 3 and the table, describe the relationship between theimage distance and the magnification produced by lens B.

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(2)

(iii) A third convex lens, lens C, is made from the same type of glass as lens B, but has ashorter focal length than lens B.

Lens B is shown in Figure 4.

Complete Figure 4 to show how lens C is different from lens B.

Figure 4

(1)

(Total 10 marks)


(a) The diagram shows a converging lens being used as a magnifying glass.

(i) On the diagram, use a ruler to draw two rays from the top of the object which showhow and where the image is formed. Represent the image by an arrow drawn at thecorrect position.

(3)

8

(ii) Use the equation in the box to calculate the magnification produced by the lens.


______________________________________________________________

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Magnification = ____________________

(2)


(b) A camera also uses a converging lens to form an image.

Describe how the image formed by the lens in a camera is different from the image formedby a lens used as a magnifying glass.

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(2)

(Total 7 marks)

A student investigated how the nature of the image depends on the position of the object in frontof a large converging lens.

The diagram shows one position for the object.

(a) Use a ruler to complete a ray diagram to show how the image of the object is formed.

(4)

9


(b) Describe the nature of this image relative to the object.

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(2)

(Total 6 marks)

(a) The diagram shows a lens used as a magnifying glass. The position of the eye is shownand the size and position of an object standing at point O.

(i) What type of lens is shown in the diagram?

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(1)

10

(ii) Two points are marked as F. What are these points?

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(1)

(iii) What is the name of the straight line which goes through the point F, through thepoint L at the centre of the lens, and through the point F on the other side?

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(1)


(iv) On the diagram, use a ruler to construct accurately the position of the image. Youshould show how you construct your ray diagram and how light appears to comefrom this image to enter the eye.

(5)

(v) The image is virtual. What is a virtual image?

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(1)

(b) The lens shown in the diagram in part (a)(iv) can be used in a camera to produce a realimage.

Explain why a real image must be produced in a camera and how the object and the lensare positioned to produce a real image which is smaller than the object.

Do not draw a ray diagram as part of your answer.

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(3)

(Total 12 marks)


The diagram shows the image IC formed by a lens, of an object OB a long way from it. Thepoints F mark the focal points of the lens.

11

(a) Describe, either by writing below or drawing on the diagram, how the size and position ofthe image changes:

(i) when the object OB is moved towards the focal point F.

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(ii) when the object OB is moved past F to a point nearer the lens than the focal point.

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(4)

(b) Explain how a converging lens in a camera is used to produce sharp images on the filmwhen the object is a long distance away from the camera, and when it is close tothe camera.

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(3)

(Total 7 marks)


Mark schemes

(a) magnification =

1

1

dividing by an object height of 1 cm gives the same (numerical) value1

(b) accept anything practical that would work eg:

use a taller object

use a (travelling) microscope

attach a scale to the screen and use a magnifying glass1

(c) both points plotted correctly1

correct line of best fit drawn

a curve passing through all points (within ½ square), judge by eye1

(d) values of 1.4 and 0.6 extracted from the graph1

2.33 times bigger

accept any number between 2.3 and 2.5 inclusive1

(e) by dividing the distance between the lens and the image by the distance between the lensand the object

1

at least one correct calculation and comparison eg 100÷25 = 4 which is the same as themeasured magnification

1

[9]


(a) (i)

1

2

(ii) 1 degree1

(iii) 1.6

allow 1 mark for correct substitution, ie 0.80 / 0.5 provided nosubsequent step shown

working showing 1.59(9…..) scores zero2

(b) 2nd diagram ticked

1

(c) (i) any one correct description:• upright• virtual• diminished.

treat multiple words as a list1

(ii) 0.25

allow 1 mark for correct substitution, ie 1 / 4 or 5 / 20 provided nosubsequent step shown

ignore any unit2

(iii) Correcting short sight1

[9]


(a) (i) answer in the range 3.0 ↔ 3.1 inclusiveaccept for 1 mark

3.6 ÷ 1.2 or 3.7 ÷ 1.2

or 36 ÷ 12 or 37 ÷ 12

or 18 ÷ 6 or 18.5 ÷ 6

or 10.2 ÷ 3.4 or 102 ÷ 34

or answer in the range but with a unit eg 3 cm2

3

(ii) (principal) focus / focal (point(s)) / foci / focus

accept ‘focusses’

accept focals

do not accept focal length1

(iii) at the intersection of virtual / imaginary rays

or ‘where virtual / imaginary rays cross’

or the rays of (real) light do not cross

or the image on the same side (of the lens) as the object

or the image is drawn as a dotted line

or the image is upright

do not accept ‘cannot be put on a screen’

do not accept any response which refers to reflected rays1

(b) (i) another correct observation about relationship between values of d

example

15 is three times bigger than 5 but1

(but) not the relationship between corresponding values for magnification

2.0 is not three times bigger than 1.21

(ii) when the distance / d increases the magnification increases

or the converse

accept ‘there is a positive correlation’

do not accept any response in terms of proportion / inverseproportion

1

(iii) (student has) no evidence (outside this range)

accept data / results / facts for ‘evidence’1

[8]


(a) converging (lens)

accept ‘con vex (lens)’

accept biconvex1

4

(b) (principal) foci

accept ‘focus’ / ‘focuses’ / ‘focis’

focal point(s)1

(c) (i) formed where (real) rays (of light) intersect / meet / cross

accept rays (of light) pass through the image

accept ‘image is on the opposite side (of the lens to the object)’

accept (construction) lines cross over

a response relating to a screen or similar is neutral

lines are solid and not dotted is neutral1

(ii) inverted

accept any unambiguous correct indication1

(d) (i) smooth curve which matches the points

judge by eye but do not accept point to point by ruler or otherwise1

(ii) continuous1

(iii) as distance increases, magnification decreases

accept negative correlation

a statement ‘inversely proportional’ is incorrect and limits maximummark for this part question to 1

1

further detail eg magnification falls steeply between 40 and 50 cmormagnification begins to level out after / at 70 cm

1

[8]

(a) (i) answer in the range 3.0 ↔ 3.1 inclusiveaccept for 1

3.6 ÷ 1.2 or 3.7 ÷ 1.2

or 36 ÷ 12 or 37 ÷ 12

or 18 ÷ 6 or 18.5 ÷ 6

or 10.2 ÷ 3.4 or 102 ÷ 34

or answer in the range but with a unit eg 3 cm2

5


(ii) (principal) focus / focal (point(s)) / foci / focus

accept ‘focusses’

accept focals

do not accept focal length1

(iii) at the intersection of virtual / imaginary rays

or ‘where virtual / imaginary rays cross’

or the rays of (real) light do not cross

or the image on the same side (of the lens) as the object

or the image is drawn as a dotted line

or the image is upright

do not accept ‘cannot be put on a screen’

do not accept any response which refers to reflected rays1

(b) (i) another correct observation about relationship between values of d (1)

(but) not the same relationship between correspondingvalues for magnification (1)

example

15 is three times bigger than 5 but

2.0 is not three times bigger than 1.22

(ii) when the distance / d increases the magnification increases

or the converse

accept ‘there is a (strong) positive correlation’

do not accept any response in terms of proportion / inverseproportion

1

(iii) (student has) no evidence (outside this range)

accept data / results / facts for ‘evidence’1

[8]

(a) Reflection correctNormal incidence correct in and outCorrect refraction inParallel ray out

each for 1 mark4

6

(b) (i) Each ray correctly refracted in

1 + 1 = 27


(ii) Wavefronts perp sidesWavefronts closer

(Cannot score wavefront marks if refracted rays clearly wrong)

(iii) Speed reducesStarting at BThen D

each for 1 mark

(c) TIR correct

gets 2 marks

Else rough reflection

gets 1 mark2

[13]

(a) the image would decrease in size1

the image would change (from virtual) to real

accept that the image (of bulb M) can be projected on to a screen1

the image would change (from non-inverted) to inverted1

7

(b) a ray through the centre of the lens

rays should be drawn with a ruler

ignore arrows1

a ray parallel to the principal axis and passing through the principal focus to the right oflens

accept solid or dashed lines

accept a ray drawn as if from the principal focus to the left of thelens, emerging parallel to the principal axis

1

image drawn where rays cross

image should be to left of the lens1


(c) (i) (because the glass in) lens A has a greater refractive index

accept lens A is more powerful

accept lens A has a shorter focal length1

(ii) when the magnification increases by 1, the image distance increases by 10 cm

accept for 1 mark it is a linear pattern

or

as the image distance increases, the magnification increases

do not accept directly proportional2

(iii) diagram showing the surfaces of a convex lens C having greater curvature than lensB

the size of the lens drawn is not important1

[10]


(a) (i) two correct rays drawn

1 mark for each correct ray

• ray parallel to axis from top of object and refracted through focus and traced back beyond object

• ray through centre of lens and traced back beyond object

• ray joining top of object to focus on left of lens taken to the lens refracted parallel to axis and traced back parallel to axis beyond object

2

8

an arrow showing the position and correct orientation of the image for their rays

to gain this mark, the arrow must go from the intersection of thetraced-back rays to the axis and the image must be on the sameside of the lens as the object and above the axis

1

(ii) (x) 3.0

accept 3.0 to 3.5 inclusiveor

correctly calculated

allow 1 mark for correct substitution into equation using their figures

ignore any units2


(b) any two from:

in a camera the image is:

• real not virtual

• inverted and not upright

accept upside down for inverted

• diminished and not magnified

accept smaller and biggeraccept converse answers but it must be clear the direction of thecomparison

both parts of each marking point are required2

[7]

(a) any two for 1 mark each

deduct (1) from the first two marks if a ruler has not been used butthe intention is clear

ray from the object's arrowhead

• through centre of lens

• parallel to the axis then, when it reaches the lens, through F on the right

• through F on the left then, when it reaches the lens parallel to the axis

example of a 4 mark response

if more than two construction lines have been drawn all must becorrect to gain 2 marks

construction lines drawn as dashed lines do not score credit2

image shown as vertical line from axis to where their rays intersect

image need not be marked with an arrowhead but, if it is, it must becorrect

1

ray direction shown

only one correct direction

arrow needed but there must not be any contradiction1

9


(b) any two from:

• inverted

accept ‘upside down’

• magnified

accept ‘bigger’

• real

accept ‘not virtual / not imaginary’

one correct feature gains 1 mark

ignore any reference to position

an incorrect feature negates a correct response2

[6]

(a) (i) converging / convex / biconvex1

(ii) focal (points) or foci

accept focuses or focus (point)1

(iii) (principal) axis1

10


(iv)

all lines drawn with a ruler for full marks

no ruler, penalise 1 mark from first four

last mark can still be awarded

double refraction drawn could get 4 out of 5 marks

ray that continues from the top of the object through Lto the eye

1

horizontal ray from the top of the object, refracted by the lensand continued through F on the r.h.s. to the eye

1

back projections of these rays (shown as dotted lines)1

image 25 mm high at 61 mm left of L(tolerance 1 mm ± vertically, 2 mm ± horizontally)

1

at least one arrow shown on real ray and towards the eyebut do not credit if contradicted by other arrow(s)

1

(v) formed where imaginary rays intersect / cross or not formed by real rays

accept (virtual image) is imaginaryaccept cannot be put on screendo not credit just ‘… is not real’

1


(b) (the image) needs to fall on film / sensors / LDRs / CCDs

accept just ‘charged couples’do not credit ‘… solar cells’do not accept virtual image cannot be stored

1

either to cause a (chemical) reaction or to be digitalised

for credit response must be appropriate to camera type1

object (should be) on the far side of F / the focus (from the lens)

or … more than the focal length (away from the lens)allow ‘beyond the focus’

or object should be more than twice the distance / 2F (from the lens) (2 marks)

or … more than twice the focal length (away from the lens)(2 marks)

1

[12]

(a) (i) Image distance increasesImage size increasesRemains invertedRemains real

for 1 mark each2

11

(ii) Image distance decreasesImage size decreasesBecomes uprightBecomes virtual

for 1 mark each2

(b) Move lens with respect to filmCloser for distant objectsFurther for near objects

for 1 mark each3

[7]


name: p6 lenses · a student investigated how the magnification produced by a convex lens varies...

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