physics review em waves & optics

7/25/2019 Physics Review EM Waves & Optics

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NAME______________________________

IB PHYSICS HL

REVIEW PACKET: OPTION HEM WAVES AND OPTICS

1. This question is about the formation of coloured fringes when white light is reflected from thin films.

(a) Name the wave phenomenon that is responsible for the formation of regions of different colour when white light is

reflected from a thin film of oil floating on water.

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(1)

(b) A film of oil of refractive index 1.45 floats on a layer of water of refractive index 1.33 and is illuminated by white light

at normal incidence.

Illumination

Air

Oil

Water

When viewed at near normal incidence a particular region of the film looks red, with an average wavelength of about 650 nm.

An equation relating this dominant average wavelength , to the minimum film thickness of the region t, is = 4nt.

(i) State what property n measures and explain why it enters into the equation.

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(2)

(ii) Calculate the minimum film thickness.

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(1)

(iii) Describe the change to the conditions for reflection that would result if the oil film was spread over a flat sheet of

glass of refractive index 1.76, rather than floating on water.

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(2)

(Total 6 marks)


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2. This question is about resolution.

(a) State the name of the wave phenomenon that limits the resolution of any optical instrument.

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(1)

(b) Explain with the aid of a diagram, the Rayleigh criterion.

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(Total 4 marks)

3. This question is about oil films.

Explain briefly the formation of coloured images when white light is reflected at a film of oil on water.

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(Total 3 marks)

4. A student uses a diffraction grating to view the visible part of the sodium emission spectrum.

(a) Explain how the diffraction grating is able to separate light into component wavelengths.

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(3)

(b) Sodium light is incident normally on a grating having 6000 lines per centimetre. Calculate the angle at which light of

wavelength 589.6 nm will be seen in the first order spectrum.

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(2)

(Total 5 marks)


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5. A student looks at two distant point sources of light. The wavelength of each source is 590 nm. The angular separation between

these two sources is 3.6 104

radians subtended at the eye. At the eye, images of the two sources are formed by the eye on the

retina.

(a) State the Rayleigh criterion for the two images on the retina to be just resolved.

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(2)

(b) Estimate the diameter of the circular aperture of the eye.

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(1)

(c) Use your estimate in (b) to determine whether the student can resolve these two sources. Explain your answer.

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(2)

(Total 5 marks)


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6. This question is about diffraction at a single slit.

Plane wavefronts of monochromatic light are incident on a narrow, rectangular slit whose width bis comparable to the

wavelength of the light. After passing through the slit, the light is brought to a focus on a screen.

Z W

Xb

Q

Y

P

slit screen

The line XY, normal to the plane of the slit, is drawn from the centre of the slit to the screen and the points PandQare the first

points of minimum intensity as measured from point Y.

The diagram also shows two rays of light incident on the screen at point P. Ray ZP leaves one edge of the slit and ray XP leaves

the centre of the slit.

The angle is small.

(a) On the diagram, label the half angular width of the central maximum of the diffraction pattern.

(1)

(b) State and explain an expression, in terms offor the path difference ZW between the rays ZP and XP.

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(2)

(c) Hence deduce that the half angular width is given by the expression

=b

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(3)

(d) In a particular demonstration of single slit diffraction,= 450 nm,b = 0.15 mm and the screen is a long way from the

slits.

Calculate the angular width of the central maximum of the diffraction pattern on the screen.

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(2)


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Using light of the same wavelength as above (450 nm), an arrangement is set up to demonstrate diffraction by a double slit. Each

slit has the same width as that above (0.15 mm) and the slit separation is d. The graph below shows the variation with the angle

of diffraction of the intensityI of the diffraction pattern on the screen.

10 5 0 5 10/ 10 rad

I/ arbitrary units

3

From the graph it can be seen that a maximum is missing at the angle = 3.0 103rad.

(e) Calculate the slit separation d.

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(2)

(Total 10 marks)

7. Monochromatic parallel light is incident on two slits of equal width and close together. After passing through the slits, the light is

brought to a focus on a screen. The diagram below shows the intensity distribution of the light on the screen.

I

distance along the screenA B

(a) Light from the same source is incident on many slits of the same width as the widths of the slits above. Draw on the

above diagram, a possible new intensity distribution of the light on the screen between the points A and B on the screen.

(2)

A parallel beam of light of wavelength 450 nm is incident at right angles on a diffraction grating. The slit spacing of the

diffraction grating is 1.25 106

m.

(b) Determine the angle between the central maximum and first order principal maximum formed by the grating.

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(2)

(Total 4 marks)


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8. This question is about X-rays.

(a) Draw a labelled diagram of an experimental arrangement for the production of X-rays.

(4)

(b) Suggest how each of the following may be controlled.

(i) Intensity of the X-ray beam

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(2)

(ii) Minimum wavelength of X-ray photons

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(2)

(c) State, and explain, the origin of the continuous part of an X-ray spectrum.

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(2)

(Total 10 marks)


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9. This question is about refractive index and critical angle.

The diagram below shows the boundary between glass and air.

glass air

(a) On the diagram, draw a ray of light to illustrate what is meant by critical angle. Mark the critical angle with the letter c.

(3)

A straight optic fibre has length 1.2 km and diameter 1.0 mm. Light is reflected along the fibre as shown below.

1.2 km

1.0 km

At each reflection, the angle of incidence is equal in value to the critical angle. The refractive index of the glass of the fibre is1.5.

(b) Deduce that the length of the light path along the optic fibre is about 1.8 km.

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(4)

The speed of light in the fibre is 2.0 108m s

1.

(c) Calculate the time for a pulse of light to travel the length of the fibre when its path is

(i) along the axis of the fibre.

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(1)

(ii) as calculated in (b).

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(1)

(Total 9 marks)


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10. This question is about spherical aberration.

The diagram below shows the image of a square grid as produced by a lens that does not cause spherical aberration.

(a) In the space below, draw a possible shape of this image, as produced by a lens that causes spherical aberration.

(2)

(b) Describe oneway in which spherical aberration can be reduced.

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(2)

(Total 4 marks)

11. This question is about the human eye.

The human eye produces images of objects that are placed between the near point and the far point of the eye.

(a) Explain what is meant by

(i) near point.

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(1)

(ii) far point.

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(1)


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The optical working of the eye may be modelled as a single lens of variable focal length. In this model, when the eye is focused on a

distant object which is not on the principal axis, the eye lens has a focal length of 1.7 cm.

(b) (i) Draw a labelled ray diagram to show how the eye lens forms an image of the distant object. (Note:this is a

sketch and does not need to be drawn to scale.)

(3)

(ii) State the distance from the lens to the image.

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(1)

To focus on an object 50 cm away from the eye, the eye lens in the model changes shape to change its focal length. This enables

the image distance to remain the same for all object distances.

(c) (i) Determine the new focal length of the eye lens.

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(2)

(ii) Suggest what change takes place in the shape of the lens in this model. Explain your answer.

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(2)

In the human eye most of the refraction actually takes place due to the change of medium from air to the cornea (the transparent

structure at the front of the eye). The following refractive indices are known.

Material Refractive index

air 1.00cornea 1.34

water 1.33

(d) (i) Explain what is meant by refractive index.

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(2)

(ii) Use the information to suggest why it is impossible for a person to see objects clearly when swimmingunderwater.

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(2)

(Total 14 marks)


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12. This question is about the simple magnifying glass.

An object O is placed in front of a converging lens in the position shown in the diagram below. The principal foci of the lens are

marked F.

principal axisF F

converging lens

O

(a) On the diagram,

(i) construct rays to locate the position of the image.

(1)

(ii) draw in the image and label it I.(1)

(iii) show on the diagram where the eye must be placed in order to view this image.

(1)

For a particular lens, the focal length is 10.0 cm and the distance of O from the lens is such that the image is formed at the near

pointof the eye. The distance of the lens from the eye is 3.0 cm.

(b) (i) Explain what is meant by the termnear point.

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(1)

(ii) Calculate the distance of the object from the lens if the near point is 25.0 cm from the eye.

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(4)

(iii) State, and explain, where the object should be placed if the image is to be formed at thefar point.

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(2)

(Total 10 marks)


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13. This question is about refractive index.

Light from a laser is directed at a semi-circular glass block. The light passes undeviated through the block and on to a screen,

forming a spot at A as shown.

Laser P

A

B

The semi-circular block is rotated about the point P. The spot of light on the screen is seen to move downwards. When the spot

reaches point B, it disappears.

(a) Complete the diagram below to show the position of the semi-circular block when the spot is at point B. The original

position of the block is shown as a dotted line.

Laser P

A

B

(1)

In a particular experiment, the distance PA is 120 cm and distance AB is 138 cm.

(b) Calculate the refractive index of the glass of the block.

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(3)

The laser is changed for one emitting light of higher frequency. The experiment is then repeated.

(c) State and explain whether the distance AB will be greater or less than 138 cm.

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(3)

(Total 7 marks)


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14. This question is about waves.

(a) Explain what is meant by

(i) monochromatic.

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(1)

(ii) coherent.

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(1)

(b) The table below compares waves from different sources. The first two rows have been completed for you. Complete thefinal three rows of the table.

electromagnetic monochromatic coherent

light from a laser Yes Yes Yes

sound from a loudspeaker No No No

light from a filament lamp

-rays from a radioactive source

infra-red rays from the Sun

(3)

(c) State an application of laser light.

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(1)

(Total 6 marks)


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15. This question is about converging lenses.

(a) The diagram shows a small object O represented by an arrow placed in front of a converginglens L. The focal points of

the lens are labelled F.

F FO

L

(i) Define thefocal pointof a converging lens.

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(2)

(ii) On the diagram above, draw rays to locate the position of the image of the object formed by the lens.(3)

(iii) Explain whether the image is real or virtual.

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(1)

(b) A convex lens of focal length 6.25 cm is used to view an ant of length 0.80 cm that is crawling on a table. The lens isheld 5.0 cm above the table.

(i) Calculate the distance of the image from the lens.

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(2)

(ii) Calculate the length of the image of the ant.

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(2)

(Total 10 marks)


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16. This question is about a compound microscope.

A compound microscope consists of two convex lenses of focal lengths 1.20 cm (lens A) and 11.0 cm (lens B). The lenses are

separated by a distance of 23.0 cm as shown below. (The diagram is not drawn to scale.)

O

1.30 cm 23.0 cm

Lens BLens Af =11.0 cmf =1.20 cm

An object O is placed 1.30 cm from lens A. An image of O in lens A is formed a distance of 15.6 cm from A.

(a) This image forms an object for lens B. Calculate the object distance for lens B.

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(1)

(b) Calculate the distance from lens B of the image as produced by lens B.

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(2)

(c) Calculate the magnification of the microscope.

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(2)

(Total 5 marks)


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17. This question is about image formation by lenses

The diagram below shows the positions of two convex lenses L1and L2used in an optical instrument. F1and F2are the

principal foci of L1and L2respectively. The object O is viewed through the two lenses.

L1

O

F1

F1

F2

I1

The diagram also shows two rays from the object O to the position of the image I 1produced in the lens L1.

(a) (i) Mark the position of the other principal focus of lens L2. Label this position F2.

(1)

(ii) The image I1acts as an object for the lens L2. Draw twoconstruction rays to locate the position of the image I 2

formed by lens L2. Label this image I2.

(3)

(b) State and explain whether the image I2is real or virtual.

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(1)

(c) State the name of this optical instrument.

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(1)

(d) State

(i) the change, if any, in the positions of the lenses so that the final image in (a) (ii) is formed at infinity;

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(2)

(ii) why the image, formed at infinity, is magnified.

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.........................................................................................................................(1)

(Total 9 marks)


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18. This question is about refraction.

A bird is hovering above a pond. A fish is in the pond at the position shown in the diagram below.

bird

surface of the pond

fish

(a) Draw rays on the diagram above to locate the position of the image of the fish as seen by the bird.

(3)

(b) Explain whether the image of the fish is real or virtual.

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(1)

(c) The fish is 48 cm below the surface of the pond. The bird hovers vertically above the fish. Calculate the apparent depth

of the fish. The refractive index of water is 1.3.

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(2)

(Total 6 marks)

19. This question is about refraction and dispersion.

(a) State what is meant by dispersion.

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(1)(b) A thin beam of white light is incident on one surface of a glass prism as shown below.

On the diagram above, draw lines to show the approximate paths of the red and of the blue light as it passes through theprism and back into the air.

(3)

(c) State and explain, with reference to your diagram, whether the refractive index of glass for blue light is greater or lessthan that for red light.

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(3)


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(d) A second similar prism is placed close to the first prism in (b) as shown below.

Suggest the appearance and the direction of the light that emerges from the second prism.

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(2)

(Total 9 marks)

20. This question is about a compound microscope.

The diagram below shows two lenses of a compound microscope. L1is the objective lens andL2is the eyepiece lens.

I L L

O

I

1 2

1

2

I1is the image of the object O formed by the objective lens L1. The final image formed is in the plane shown by the dotted line

labelledI2.

(a) On the diagram above, construct a ray orrays to determine the position of the principal focus of the eyepiece. Label this

position with the letter F.

(2)


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(b) By using the grid, take measurements to determine the linear magnification of

(i) the objective lens.

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(1)

(ii) the eyepiece.

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(1)

(c) Use your answer to (b) to determine the total linear magnification of the microscope.

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(1)

(Total 5 marks)


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MARK SCHEME!

1. (a) interference; 1 max

Award no marks for diffraction.

(b) (i) nis the refractive index of the oil;the wavelength in the medium is reduced / depends on n; 2 max

(ii) t=)45.14(

650

= 110 nm; 1 max

Award[0]for use of incorrect refractive index.

(iii) Weakanswergivingsomeindication.

that the rays reflected off the bottom of the oil film now shift /

change in phase by2

()

Abetterdefinedstatement.

that initially the rays reflected off the bottom of the oil film (on water),

did not suffer a phase change;

but now do shift in phase by

2

() 2 max

[6]

2. (a) diffraction / bending of waves (due to an aperture / obstacle); 1 max

(b) the Rayleigh Criterion is used to establish when the images of

two objects are just resolved;the minimum of one diffraction pattern falls on the maximum of the other;

relevant diagram; 3 max

Minimum of one diffraction pattern

falls on the maximum of the other.

Note that a well labelled and annotated diagram could receive up to[2 max].

[4]

3. light gets reflected from oil / air and oil / water interfaces;

these reflected rays interfere, because there is a path difference between them;

caused by the thickness of the oil film / the different index of refraction for

different wavelengths (dispersion);the colour seen is white light minus that colour which suffers destructiveinterference / the colour seen is that which suffers constructive interference; 3 max

Award[3 max]for any three points above.

[3]


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4. (a) identification of path length differences from slit to slit;to give constructive interference at a particular angle for a

particular wavelength;thus different wavelengths will constructively interfere at different

angles ielight will be separated in component wavelengths; 3 max

Award full marks for other explanations not of this format but the response must explain the creationof the spectrum.

(b) correct substitution into n= dsin ;

to give sin = 5.896 107

600 000 = 0.35376 so = 20.7 21; 2

[5]

5. (a) the diffraction pattern of one point source has its central maximum on the firstminimum of the diffraction pattern of the other point source / OWTTE; 2

Full marks can be awarded for a clearly drawn and fully labelled diagram.

Partial credit is for answers that have some idea but lack precision.

(b) 3 (2) mm; 1

(c) correct calculation of Rayleigh criteria angle;

eg= 1.22d

= 1.22 590 10

9/ 0.003= 2.4 10

4radians.

Accept answers that miss the factor of 1.2 to get 2.0 104

radians.

correct comparison and answer; 2 max

eg this will be resolved as minimum angle is less than the separation of the point sources.

Watch for ecf this angle may or may not be resolved depending on the estimation of the diameter

of the aperture.[5]

6. (a) YXP; 1

(b)2

;

for the waves to interfere destructively at P, their path difference must

be

2

1n

and since this is the first minimum n= 0 / OWTTE; 2

Look for some reasonable justification for the second mark.

(c) = with some justification, such as angles are small / screen is far away;

=

2

b

ZW;

sinceZW=2

, =

b

; 3

Allow use of single slit diffraction formula b sin = nif it is clear that the candidate knows what

they are doing, ie they are not using the diffraction grating formula. n =1, is small, with a

justification, so sin, =b

.

(d) =4

7

105.1

105.4

= 3.0 10

3rad;

angular width = 6.0 103

rad; 2

(e) recognize to use d= nwith n= 4;

d=3

7

100.3

105.44

= 6.0 10

4m;

or

recognize for missing orders thatb

d= 4;

so d= 4b= 6.0 104

m; 2 max

Award[1 max]if n = 3 is used.

[10]


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7. (a) same number of maxima at the same place but much sharper;

greater intensity than double slit / presence of small maxima in between maxima; 2

(b) sin =d

;

= 0.36 to give = 21; 2

[4]

8. (a) Labelled diagram showing:evacuated envelope;

metal target;heated filament;

anode and cathode clear; 4

Anode, cathode and heating of filament may be indicated by electrical symbols.

(b) (i) change temperature of cathode / cathode current;

increase temperature / current gives increase in intensity; 2

or

change (accelerating) voltage / atomic number of target;

increase voltage / atomic number gives increase in intensity;

(ii) change accelerating p.d. / anode-cathode p.d.;

increase p.d. gives shorter wavelength; 2

(c) whenever a charged particle is accelerated / interacts with matter,

it radiates electromagnetic radiation;accelerations of all different magnitudes so many different

wavelengths produced; 2

[10]

9. (a) light incident from glass;

emergent ray along boundary;

c marked correctly; 3

(b) sin c =5.1

1 ;

for every 1.0 mm length, light travels 1.5 mm;

path length = 1.2 108 1.5

= 1.8 km; 4

Award[4]for any correct calculation that leads to 1.8 km.

(c) (i) time =8100.2

1200

= 6.0 s; 1

(ii) time = 9.0 s; 1

[9]


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10. (a)

straight-line cross;

four outersides curving outwards; 2

Accept curving of lines in the opposite way or fuzzy in centre and focussed at edges or vice versa.

(b) basic statement eguse two thin lenses / stop down to use onlyparaxial rays;

further detail egsame f as the fatter lens; 2

[4]

11. (a) (i) the position of the closest object that can be brought into focus by the

unaided eye / OWTTE; 1

Accept the distance to the closest object etc

(ii) the position of the furthest object that can be brought into focus by the

unaided eye / OWTTE; 1

Accept the distance to the furthest object etc

(b) (i) two (or more) parallel rays into lens;which all converge after refraction at the lens;

correctly off axis; 3

Award benefit of doubt if no arrows on rays.

lens

Award[2 max]for a correct ray diagram showing rays diverging from an object at twice the focal

length (or more) from the lens.

(ii) about 1.7 cm; 1

(c) (i) use of the lens equation with u= 50 cm, v= 1.7 cm;

to getf = 1.64 1.6 cm; 2

Award[1 max]for a scale diagram since accuracy is inappropriate.

(ii) lens gets fatter / OWTTE;since focal length goes down; 2

(d) (i) ratio of speed of EM waves;

in vacuum to their speed in medium;

Award[0]for quoting from the data booklet without additional information.

ordefinition as ratio of sin (angle of incidence) to sin (angle of refraction);explanation of how these angles are measured; 2

(ii) normally the refraction is from air to cornea and the difference in

refractive index is large;

if under water refraction is from water to cornea and the difference inrefractive index is negligible so no image is formed / OWTTE;

or

rays crossing the water-eye boundary will undergo little refraction

since the ns are nearly equal;

hence, rays cannot be brought to a focus (focussed); 2

[14]


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12. (a)

principal axisF F

converging lens

OI

Eye

(i) two appropriate rays; 1 max

(ii) correct image position; 1 max

(iii) eye to the right of the lens; 1 max

(b) (i) if the object is nearer than this to the eye then the eye cannotfocus it clearly / OWTTE; 1 max

(ii)fvu

111 ;

v= (25 3)cm = 22 cm

10

1

22

11

u:

to give u= 6.9 cm; 4 max

Alternatively for scale drawing award[1]for scale,[2]for rays,[1]for position of image

and[1]for subtraction.

(iii) at the focal point;the far point is at infinity; 2 max

[10]

13. (a) diagram showing ray emerging along flat face; 1

(b) tan =120

138, = 49.0;

critical angle = 41.0;

n =Csin

1 = 1.52; (allow ecf if sensible) 3

Award[1 max]if the critical angle is = 49.0

(answer n =Csin

1= 1.33).

(c) nis greater at higher frequency;so Cis smaller;

henceAB is larger; 3

Award[2]if logic totally reversed.

[7]


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14. (a) (i) single frequency / single colour / OWTTE; 1

(ii) waves with a constant / predictable phase / OWTTE; 1

Be generous as it is hard to describe in a few words. Look for understanding.

(b) Award[1]for each correct row or column, up to[3 max]. 3 max

Electromagnetic Monochromatic Coherent

light from a laser

sound from a loudspeaker

light from a filament lamp Yes No No-rays from a radioactive source Yes Yes / No No

infra-red rays from the Sun Yes No No

(c) any general application of laser light; 1

To achieve[1] it must be a situation where the use of laser light is appropriate and there

is sufficient outline detail to understand the situation. Accept any use (so long as notambiguous) without description.

[6]

15. (a)

F FO

L

image

(i) it is the point on the principal axis;through which a ray parallel to the principal axis passes after going

through the lens; 2

Award[0]if focal point is defined as a distance.

(ii) Award[2]foranytwoappropriateraysand[1]forcorrect

positioningoftheimage(upright). 3

(iii) it is virtual because no rays pass through the image / cannot be formed

on a screen; 1

Award[0] if no explanation is provided.

(b) (i)fvu

111

0.5

1

25.6

11

v

;

v= 25 cm, so distance is 25 cm; 2

Accept negative sign in answer for distance.

(ii) M=u

v

M=5

25= 5

5

u

vMAccept

L= 5 0.8 = 4.0 cm; 2[10]


25/26

25

16. (a) u= 23.0 15.6 = 7.4 cm; 1

(b)4.7

1

0.11

11

v;

v= 22.6 cm, so distance is 22.6 cm; 2

Accept negative sign in answer for distance.

(c) M=3.1

6.15

4.7

6.22

;

M= 36.7 37; 2

Award[0]for adding the individual magnifications to get 15.

[5]

17. (a) (i) correct position by eye but within 5mm; 1

(ii) ray parallel to principal axis through F2;

ray undeviated through pole of lens;

correct extrapolation to marked image; 3

Do not allow unless image lies between L1and right-hand F1.

(b) virtual because rays only appear to come from it; 1

(c) (compound) microscope; 1

(d) (i) L1unchanged;

L2moved (to right) so that I1is at F2; 2

(ii) angle (subtended) at eye by image is larger than that (subtended)by object; 1

[9]

18. (a) (i)

one ray from fish with correct refraction;2nd ray from fish with correct refraction;

rays backward to give correct position of image; 3

Here only a qualitative explanation (diagram) is expected,since no numerical values are given. A quantitative solution

is asked for in part (a)(iii).

(ii) virtual since extension of rays gives its position / appear to come

from fish / OWTTE; 1

(iii) ;depthapparent

depthrealn

apparent depth = ;cm373.1

48 2

[6]


26/26

19. (a) light (that is a combination of colors / wavelengths / frequencies) is divided/ split into its component colours / wavelengths / frequencies; 1

(b)

bends towards the normal at first surface;away from normal at second;

blue is deviated to a greater degree than red at both interfaces; 3Normals do not need to be drawn

Award[1 max]if dispersion is shown at second face only.

(c) refraction angle for blue light is less than for red light (at the first boundary);

since ;sin

sin

r

in

nfor blue is greater / nfor red is less; 3

Do not award marks for bald answers or answers with fallacious argument.Allow ecf for consistent argument for switching of B and R from (b).

(d) recombined / white light;

parallel to the incoming beam; 2

ignore displacement and / or rays within block

[9]

20. (a)

two correct construction rays;dotted lines back toI2to give F, 4.5(1)cm fromL2; 2

(b) (i) 2; 1

(ii) 3; 1

(c) 6; 1

[5]

physics review em waves & optics

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