Light (Cambridge International IGCSE Physics): Exam Questions

Extract:

Question stem:

• On the diagram, u = 5.0 cm and v = 7.5 cm
• The diagram is drawn to 1/5 scale, so U = 5.0 × 5 = 25 cm and V = 7.5 × 5 = 37.5 cm

When marking this answer:

• In part (i), the mark needs both U and V correct
• In part (ii), accept f₁ correctly calculated from the candidate's own U and V (ecf), for example 15.1 cm from V = 38 cm
• In part (ii), f₁ must be given to two or three significant figures and with the unit cm; a bare 15 with no unit does not earn the mark
• In part (iii), "move the screen slowly" or "move the screen backwards and forwards" each earns the mark on its own

Some students determine the focal length of a converging lens by two different methods. They use the apparatus shown in Fig. 2.1.

A student sets the distance U between the illuminated triangle and the lens.

She moves the screen until a sharp image of the triangle is seen on the screen.

Method 1

On Fig. 2.1, the distance u between the illuminated triangle and the lens is $5 . 0 \text{cm}$.

On Fig. 2.1, the distance v between the lens and the screen is $7 . 5 \text{cm}$.

Fig. 2.1 is drawn to 1/5 scale.

(i) Calculate the actual distance U between the illuminated triangle and the lens, and the actual distance V between the lens and the screen, in the experiment.

U = ...............................................................

V = ...............................................................

(ii) Calculate a value $f_{1}$ for the focal length of the lens, using the equation:

f_{1} = \frac{UV}{\left(U + V\right)}

$f_{1}$ = .........................................................

(iii) Briefly describe a technique to obtain an image on the screen that is as sharp as possible in this experiment.

Extract:

Question stem:

• From part (a): on the diagram v = 7.5 cm and the diagram is drawn to 1/5 scale, so V = 7.5 × 5 = 37.5 cm
• h_O = 1.5 cm and h_I = 2.4 cm

When marking this answer:

• In part (i), M = 1.6 must be given without a unit; an answer with a unit does not earn the mark
• In part (ii), accept 14 cm or 14.4 cm for f₂ (from V = 37.5 cm) as well as 15 cm or 14.6 cm (from V = 38 cm)
• In part (ii), accept f₂ correctly calculated from the candidate's own V and M (ecf)
• In part (ii), the unit is not required for the mark

Method 2

On Fig. 2.2, the height $h_{O}$ of the illuminated triangle is measured to be $1 . 5 \text{cm}$.

On Fig. 2.3, the height $h_{I}$ of the image on the screen is measured to be $2 . 4 \text{cm}$.

(i) Calculate a value for the magnification M, using the equation:

$M = \frac{h_{I}}{h_{O}}$

M = .........................................................

(ii) Calculate a second value $f_{2}$ for the focal length of the lens, using the value of V from (a)(i) and the equation:

f_{2} = \frac{V}{\left(M + 1\right)}

$f_{2}$ = .........................................................

Extract:

Question stem:

Some students determine the focal length of a converging lens by two methods, using an illuminated triangle, a converging lens and a screen on a bench. Method 1 uses the distances U (triangle to lens) and V (lens to screen); Method 2 uses the heights of the triangle and of its image on the screen.

When marking this answer:

• Award the mark for any one precaution from the mark scheme list
• Vague answers such as "be careful" or "measure accurately" do not earn the mark

State one precaution that could be taken to ensure that the measurements in the experiment are taken as reliably as possible.

A student is determining the refractive index n of the material of a transparent block.

Fig. 3.1 shows the outline ABCD of the transparent block.

(i) On Fig. 3.1:

• draw a normal NL at the centre of side AB

  • continue the normal so that it passes through side CD of the block
  • label the point F where NL crosses AB
  • label the point G where NL crosses CD.

(ii) Draw a line EF at an angle i = 30° to the left of the normal and above side AB.

(iii) Mark the positions of two pins P₁ and P₂ on line EF placed at a suitable distance apart for this type of ray-tracing experiment.

Extract:

A student is determining the refractive index n of the material of a transparent block.

Fig. 3.1 shows the outline ABCD of the transparent block.

(i) On Fig. 3.1:

• draw a normal NL at the centre of side AB
• continue the normal so that it passes through side CD of the block
• label the point F where NL crosses AB
• label the point G where NL crosses CD.

(ii) Draw a line EF at an angle i = 30° to the left of the normal and above side AB.

(iii) Mark the positions of two pins P1 and P2 on line EF placed at a suitable distance apart for this type of ray-tracing experiment.

The student observes the images of P₁ and P₂ through side CD of the block so that the images of P₁ and P₂ appear one behind the other.

He places two pins P₃ and P₄ between his eye and the block so that P₃, P₄ and the images of P₁ and P₂ seen through the block, appear one behind the other.

The positions of P₃ and P₄ are marked on Fig. 3.1.

(i) Draw a line joining the positions of P₃ and P₄. Continue the line until it meets the normal NL.

Label the point H where the line meets side CD. Draw the line FH.

(ii) Measure and record the length a* of the line GH.

a = ........................................................ [1]

(iii) Measure and record the length b of the line FH.

b = ........................................................ [1]

(iv) Calculate the refractive index n using the following equation:

$n=\frac{0.5b}{a}$.

n = ........................................................ [1]

Extract:

The student observes the images of P₁ and P₂ through side CD of the block so that the images of P₁ and P₂ appear one behind the other.

He places two pins P₃ and P₄ between his eye and the block so that P₃, P₄ and the images of P₁ and P₂ seen through the block, appear one behind the other.

The positions of P₃ and P₄ are marked on Fig. 3.1.

Extended tier only

The student repeats the procedure using the angle of incidence i = 45°.

a = 3.2 cm

b = 6.9 cm

Calculate the refractive index n, using the equation $n=\frac{0.71b}{a}$.

n = ........................................................

Extract:

A student is determining the refractive index n of the material of a transparent block.

(i) On Fig. 3.1:

• draw a normal NL at the centre of side AB
• continue the normal so that it passes through side CD of the block
• label the point F where NL crosses AB
• label the point G where NL crosses CD.

(ii) Draw a line EF at an angle i = 30° to the left of the normal and above side AB.

(iii) Mark the positions of two pins P1 and P2 on line EF placed at a suitable distance apart for this type of ray-tracing experiment.

The student observes the images of P1 and P2 through side CD of the block so that the images of P1 and P2 appear one behind the other. He places two pins P3 and P4 between his eye and the block so that P3, P4 and the images of P1 and P2 seen through the block, appear one behind the other. The positions of P3 and P4 are marked on Fig. 3.1.

(i) Draw a line joining the positions of P3 and P4. Continue the line until it meets the normal NL. Label the point H where the line meets side CD. Draw the line FH.

(ii) Measure and record the length a of the line GH.

(iii) Measure and record the length b of the line FH.

(iv) Calculate the refractive index n using the following equation:

n = (0.5 b) / a.

The student expected the two values of refractive index n obtained in this experiment to be equal.

State two difficulties with this type of experiment that could explain any difference in the two values of n.

Extract:

A student is determining the refractive index n of the material of a transparent block.

(i) On Fig. 3.1:

• draw a normal NL at the centre of side AB
• continue the normal so that it passes through side CD of the block
• label the point F where NL crosses AB
• label the point G where NL crosses CD.

(ii) Draw a line EF at an angle i = 30° to the left of the normal and above side AB.

(iii) Mark the positions of two pins P1 and P2 on line EF placed at a suitable distance apart for this type of ray-tracing experiment.

The student observes the images of P1 and P2 through side CD of the block so that the images of P1 and P2 appear one behind the other.

He places two pins P3 and P4 between his eye and the block so that P3, P4 and the images of P1 and P2 seen through the block, appear one behind the other.

The positions of P3 and P4 are marked on Fig. 3.1.

A student suggests precautions to take in this experiment to obtain reliable results. Tick one box to indicate the most sensible suggestion.

square Carry out the experiment in a darkened room.

square Use pins that are taller than the height of the block.

square View the bases of the pins.

square View the pins with one eye closed.

A student investigates the position of the image in a plane mirror.

Fig. 3.1 shows the ray-trace sheet he uses.

The student draws the line MR.

• He draws a normal NL to this line that passes through the centre of MR.

• He labels the point at which NL crosses MR with the letter B.

• He draws a line from B at an angle of incidence i = 30° to the normal below MR and to the left of the normal. He labels the end of this line A.

• He places a pin P₁ on line AB, as shown in Fig. 3.1. He places another pin P₂ on the line AB.

• He places the reflecting face of the mirror vertically on the line MR.

• He views the images of pins P₁ and P₂ from the direction indicated by the eye in Fig. 3.1.

(i) On Fig. 3.1, mark with a cross a suitable position for pin P₂ in this experiment.

(ii) He places two pins P₃ and P₄ some distance apart so that pin P₃ and the images of P₂ and P₁ all appear exactly behind pin P₄. The positions of P₃ and P₄ are shown on Fig. 3.1.

Draw the line joining the positions of P₃ and P₄. Continue the line until it extends at least 7.0 cm beyond MR.

Extract:

A student investigates the position of the image in a plane mirror.

Fig. 3.1 shows the ray-trace sheet he uses.

The student draws the line MR.

• He draws a normal NL to this line that passes through the centre of MR.

• He labels the point at which NL crosses MR with the letter B.

• He draws a line from B at an angle of incidence i = 30° to the normal below MR and to the left of the normal. He labels the end of this line A.

• He places a pin P₁ on line AB, as shown in Fig. 3.1. He places another pin P₂ on the line AB.

• He places the reflecting face of the mirror vertically on the line MR.

• He views the images of pins P₁ and P₂ from the direction indicated by the eye in Fig. 3.1.

(i) On Fig. 3.1, mark with a cross a suitable position for pin P₂ in this experiment.

(ii) He places two pins P₃ and P₄ some distance apart so that pin P₃ and the images of P₂ and P₁ all appear exactly behind pin P₄. The positions of P₃ and P₄ are shown on Fig. 3.1.

The student keeps pin P₁ in the same position but moves pin P₂ so that the angle of incidence i = 40°.

• The pin positions P₅ and P₆ for the reflected ray are marked on Fig. 3.1.

(i) Draw the line joining the positions of P₅ and P₆. Continue the line until it extends at least 7.0 cm beyond MR.

Label with the letter Y the point where the two lines cross beyond MR.

(ii) Draw a line from P₁ to MR that meets MR at a right angle. Measure and record the length a of this line.

a = ..................................................... [1]

(iii) Draw a line from the point labelled Y to MR that meets MR at a right angle. Measure and record the length b of this line.

b = ..................................................... [1]

The student removes all the pins. He places pin P₇ on the normal at a distance 6.0 cm from the front of the mirror.

• He views the image of P₇ in the mirror.
• He places pin P₈ on the normal behind the mirror.
• He adjusts the position of P₈ so that the image of the bottom of the pin P₇ and the top of pin P₈ seen over the mirror appear as one pin when viewed from all angles in front of the mirror.

(i) On Fig. 3.1, measure the distance x along the normal between P₈ and the mirror.

x = ..................................................... [1]

(ii) Complete the diagram in Fig. 3.2 to show the appearance of the image of pin P₇ and pin P₈ as described in (c).

Extract:

(from part b) Distance a measured correctly to within ± 2 mm; [1 mark] - In our diagram a = 5.2 cm OR 52 mm Distance b measured correctly to within ± 2 mm; [1 mark] - In our diagram a = 4.9 cm OR 49 mm (from part c) On our diagram the distance x = 5.9 cm

The student expects the readings to show that the image formed in a plane mirror is the same distance behind the mirror as the object is in front of the mirror. Readings of a = b and *x *= 6.0 cm will show this.

State whether your readings show that the image formed in a plane mirror is the same distance behind the mirror as the object is in front of the mirror. Justify your statement by reference to the readings.

statement:

justification:

Extract:

A student investigates the position of the image in a plane mirror.

The student draws the line MR.

• He draws a normal NL to this line that passes through the centre of MR.

• He labels the point at which NL crosses MR with the letter B.

• He draws a line from B at an angle of incidence i = 30° to the normal below MR and to the left of the normal. He labels the end of this line A.

• He places a pin P1 on line AB, as shown in Fig. 3.1. He places another pin P2 on the line AB.

• He places the reflecting face of the mirror vertically on the line MR.

• He views the images of pins P1 and P2 from the direction indicated by the eye in Fig. 3.1.

A student carefully carries out an investigation into an image showing the position of different pins in a plane mirror.

Suggest a practical reason why the results may not be accurate.

A student is investigating the reflection of light by a plane mirror.

Fig. 1.1 shows his ray-trace sheet at full size.

The student carries out an initial experiment. He draws lines AB and CD as shown in Fig. 1.1. He then draws a line EF through a point N as shown in Fig. 1.1 and at an angle θ to line AB.

The angle θ is

measured to be 23° ±1°

Draw a normal to line AB at point N and extend the normal to line CD. Label the point at which the normal crosses line CD with the letter L.

Extract:

A student is investigating the reflection of light by a plane mirror.

Fig. 1.1 shows his ray-trace sheet at full size.

The student carries out an initial experiment. He draws lines AB and CD as shown in Fig. 1.1. He then draws a line EF through a point N as shown in Fig. 1.1 and at an angle θ to line AB.

The angle θ is measured to be 23° ±1°

Draw a normal to line AB at point N and extend the normal to line CD.

The student places a plane mirror on line EF and a screen with a 2 mm slit on line CD. He arranges the screen so that a ray of light shines along line LN. The ray reflected from the mirror passes through point P.

State and explain whether point P, shown on Fig. 1.1, is at a suitable distance from point N for this investigation.

Extract:

A student is investigating the reflection of light by a plane mirror.

Fig. 1.1 shows his ray-trace sheet at full size.

The student carries out an initial experiment. He draws lines AB and CD as shown in Fig. 1.1. He then draws a line EF through a point N as shown in Fig. 1.1 and at an angle θ to line AB.

The angle θ is

measured to be 23° ±1°

Draw a normal to line AB at point N and extend the normal to line CD. Label the point at which the normal crosses line CD with the letter L.

(i) Draw a line joining point N and point P. Extend this line until it meets line CD.

Label the point at which this line meets line CD with the letter G.

(ii) Measure the length a of line LG.

a = ................................................... cm [1]

Extract:

A student is investigating the reflection of light by a plane mirror.

Fig. 1.1 shows his ray-trace sheet at full size.

The student carries out an initial experiment. He draws lines AB and CD as shown in Fig. 1.1. He then draws a line EF through a point N as shown in Fig. 1.1 and at an angle θ to line AB.

The angle θ is measured to be 23° ±1°

Draw a normal to line AB at point N and extend the normal to line CD.

The student repeats the procedure for values of θ = 25°, 20°, 15°, 10° and 5°. His values for a are shown in Table 1.1.

Table 1.1

Use the values from Table 1.1 to plot a graph of *a */ cm (y-axis) against *θ */ ° (x-axis).

Extract:

A student is investigating the reflection of light by a plane mirror. The student draws lines AB and CD on a ray-trace sheet, draws a line EF through a point N at an angle θ to AB, and draws a normal to AB at N. The angle θ is measured (e.g., 23° ±1°). A plane mirror is placed on EF, and a screen with a 2 mm slit is placed on CD. A ray of light shines along LN, is reflected from the mirror, and passes through point P. The student joins N and P, extends the line to meet CD at G, and measures the length a of LG. The procedure is repeated for θ = 25°, 20°, 15°, 10°, and 5°, and the corresponding values of a are recorded in a table. The values are then plotted on a graph of a (y-axis) against θ (x-axis).

Suggest a possible source of inaccuracy in this experiment, even if it is carried out carefully.

Extract:

(ii) Measure the length a of line LG.

a = ................................................... cm

The student repeats the procedure for values of θ = 25°, 20°, 15°, 10° and 5°. His values for a are shown in Table 1.1.

Table 1.1

| θ / ° | *a */cm | | 25 | 12.2 | | 20 | 8.3 | | 15 | 5.7 | | 10 | 3.6 | | 5 | 1.8 |

A student wishes to check if his values for a are reliable.

Suggest how he could improve the experiment, using the same apparatus, to check the reliability of his results.

A student is determining the focal length f of a lens.

Fig. 3.1 shows the apparatus.

The student places the screen a distance* D *= 70.0 cm from the illuminated object.

He places the lens close to the screen and moves the lens slowly away from the screen until a clearly focused image is formed on the screen.

He measures the distance u between the centre of the lens and the illuminated object.

He measures the distance v between the centre of the lens and the screen.

He repeats the procedure using values for D of 75.0 cm, 80.0 cm, 85.0 cm and 90.0 cm.

The readings are shown in Table 3.1.

Calculate, and record in Table 3.1, uv for each value of D.

Table 3.1

Extract:

Table 3.1

| D/cm | u/cm | v/cm | uv/cm^2 | | 70.0 | 22.0 | 48.4 | 1065 | | 75.0 | 20.7 | 54.5 | 1128 | | 80.0 | 20.0 | 60.0 | 1200 | | 85.0 | 19.5 | 65.8 | 1283 | | 90.0 | 19.0 | 71.2 | 1353 |

Plot a graph of* uv*/cm² (y-axis) against D/cm (x-axis). You do not need to start your axes at the origin (0,0).

Extract:

A student is determining the focal length f of a lens.

The student places the screen a distance* D *= 70.0 cm from the illuminated object.

He places the lens close to the screen and moves the lens slowly away from the screen until a clearly focused image is formed on the screen.

He measures the distance u between the centre of the lens and the illuminated object.

He measures the distance v between the centre of the lens and the screen.

He repeats the procedure using values for D of 75.0 cm, 80.0 cm, 85.0 cm and 90.0 cm.

The readings are shown in Table 3.1.

| D/cm | u/cm | v/cm | uv/cm^2^ | | 70.0 | 22.0 | 48.4 | 1065 | | 75.0 | 20.7 | 54.5 | 1128 | | 80.0 | 20.0 | 60.0 | 1200 | | 85.0 | 19.5 | 65.8 | 1283 | | 90.0 | 19.0 | 71.2 | 1353 |

Plot a graph of* uv*/cm^2^ (y-axis) against D/cm (x-axis). You do not need to start your axes at the origin (0,0).

Determine the gradient G of the line. Show clearly on the graph how you obtained the necessary information.

State the coordinates at the top and bottom of the triangle:

• (x₁, y₁) = (85, 1283)
• (x₂, y₂) = (75, 1128)

Recall the equation to calculate the gradient of a straight line:

• Gradient, G = Change in y / Change in x = (y₁ - y₂) / (x₁ - x₂)

Substitute the coordinates into the equation to calculate the gradient, G:

• G = (1283 - 1128) / (85 - 75)
• G = 15.5

Remember the following when creating your gradient triangle:

• Make it as large as possible
• Use points that the line of best fit goes through as the start and end
• Form the triangle in the middle but continue the lines onto the horizontal and vertical axis, so it is easier to read the coordinates if you need to

Determine the gradient G of the line. Show clearly on the graph how you obtained the necessary information.

G = ........................................................

Extract:

State the coordinates at the top and bottom of the triangle:

• (x₁, y₁) = (85, 1283)
• (x₂, y₂) = (75, 1128)

Recall the equation to calculate the gradient of a straight line:

• Gradient, G = (Change in y) / (Change in x) = (y₁ - y₂) / (x₁ - x₂)

Substitute the coordinates into the equation to calculate the gradient, G:

• G = (1283 - 1128) / (85 - 75)
• G = 15.5

The focal length f of the lens is numerically equal to the gradient G of the graph. Write down a value for the focal length f of the lens. Give your answer to a suitable number of significant figures for this experiment.

f = .........................................................

Extract:

A student is determining the focal length f of a lens.

Fig. 3.1 shows the apparatus.

The student places the screen a distance* D *= 70.0 cm from the illuminated object.

He places the lens close to the screen and moves the lens slowly away from the screen until a clearly focused image is formed on the screen.

He measures the distance u between the centre of the lens and the illuminated object.

He measures the distance v between the centre of the lens and the screen.

He repeats the procedure using values for D of 75.0 cm, 80.0 cm, 85.0 cm and 90.0 cm.

Suggest two difficulties in this experiment when trying to obtain accurate readings.

A student is determining the focal length of a lens.

Fig. 3.1 shows the apparatus used.

The student adjusts the position of the screen until a clearly focused image is formed on the screen.

The distance v on Fig. 3.1 is measured to be 5.80 cm.

(i) Fig. 3.1 is drawn 1/5^th actual size.

Calculate V, the actual distance from the lens to the screen

V = ......................................................... [1]

(ii) With a clearly focused image formed on the screen, the actual distance from the centre of the lens to the illuminated object, U is 20.0 cm.

Calculate the focal length f₁ of the lens using the equation $f_{1} = \frac{U V}{( U + V )}$

f₁ = ......................................................... [2]

Extract:

(ii) With a clearly focused image formed on the screen, the actual distance from the centre of the lens to the illuminated object, U is 20.0 cm. Calculate the focal length f_1 of the lens using the equation f_1 = (U V) / (U + V)

Substitute the known quantities into the equation for f_1: f_1 = (20 × 29) / (20 + 29) Calculate f_1: f_1 = 11.83 cm = 11.8 cm (3 s.f.)

The student repeats the procedure in (a), using a different distance U. She obtains another value for the focal length f₂.

f₂ = 12.2 cm

Calculate the average value f_A of the focal length of the lens, using f₂ and your value for f₁* *in (a)(ii). Give your answer to a suitable number of significant figures for this experiment.

f_A = .........................................................

Extract:

the actual distance from the centre of the lens to the illuminated object, U is 20.0 cm.

The student states that taking more measurements improves the reliability of the value obtained for f_A.

Suggest additional values for U that you would use.

Extract:

A student is determining the focal length of a lens. The student adjusts the position of the screen until a clearly focused image is formed on the screen. The distance V is measured from the lens to the screen. The actual distance from the centre of the lens to the illuminated object, U, is also measured. The experiment involves measuring U and V to calculate the focal length of the lens.

State two precautions that you would take in this experiment to obtain accurate readings.

A student investigates the magnification produced by a converging lens.

He is using the apparatus shown in Fig. 3.1.

The illuminated object consists of a triangular-shaped hole in a piece of card. Fig. 3.2 shows, full size, the illuminated object.

Measure and record the height h_O of the triangular-shaped hole.

h_O = .....................................................  cm

Extract:

The height of h_O is: 1.4 cm; [1 mark]

Using your results from (a) and the equation M = h_O / h_I, calculate a value M and record this value in Table 3.1.

Extended Tier Only

The distance between the illuminated object and the centre of the lens is set to u = 20.0 cm. The screen is moved until a focused image of the illuminated object is seen, as shown in Fig. 3.3.

The student repeats the procedure for u = 30.0 cm, u = 40.0 cm, *u *= 50.0 cm and u = 60.0 cm. His results are shown in Table 3.1.

Measure, and record in the first row of Table 3.1, the height h_I of the image.

Using your results from (a) and the equation* *$M=\frac{h_{o}}{h_{I}}$, calculate a value M and record this value in Table 3.1.

Table 3.1

Extract:

Table 3.1

| u / cm | h_I / cm | M | | 20.0 | 4.5 | 0.31 | | 30.0 | 1.5 | 0.93 | | 40.0 | 0.9 | 1.6 | | 50.0 | 0.6 | 2.3 | | 60.0 | 0.5 | 2.8 |

Plot a graph of u/cm (y-axis) against M (x-axis).

You do not have to start your axes at the origin (0, 0)

Extract:

Plot a graph of u/cm (y-axis) against M (x-axis).

You do not have to start your axes at the origin (0, 0)

• Axes with correct orientation, both labelled with quantity and unit; [1 mark]
• Appropriate scales (plots occupying at least ½ grid); [1 mark]
• Plots all correct to ½ small square and precise plots; [1 mark]
• Well-judged line and thin line; [1 mark]

[Total: 4 marks]

When drawing a line of best fit on a graph have roughly even numbers of data points above and below the line. If not possible, try and ensure the combined distances of points above the line equal the combined distances of points below.

Here, only one point is below the line while two are above, but the point below the line is further from the line than the two points above.

Determine the gradient G of the graph.

Show clearly on the graph how you obtained the necessary information.

G = ....................................................

Extract:

The distance between the illuminated object and the centre of the lens is set to u = 20.0 cm. The screen is moved until a focused image of the illuminated object is seen, as shown in Fig. 3.3.

The student repeats the procedure for u = 30.0 cm, u = 40.0 cm, u = 50.0 cm and u = 60.0 cm. His results are shown in Table 3.1.

Measure, and record in the first row of Table 3.1, the height h_I of the image.

Extended Tier Only

Describe one difficulty that might be experienced when measuring the height of the image h_I .

Suggest an improvement to the apparatus to reduce this difficulty.