O Level Physics 5054 Paper 42, May/June 2025

On Fig. 1.1, draw a normal to the block at the point R. Extend your normal $6\text{ cm}$ above side AD and below side BC. Label the point where the normal crosses side BC of the block with the letter T. Measure the angle $\theta$ between SR and the normal. $\theta ={\text{........................................................}}^{\circ }$

The student: • positions an illuminated slit on the ray-trace sheet so that a ray of light passes along the line SR towards R • marks with small crosses (x) two points on the ray that leaves side BC of the block • removes the transparent block. On Fig. 1.1, draw a straight line through the two crosses to meet side BC of the block. Label the point where this line meets side BC with the letter E. Label the other end of this line as F. Draw a straight line from E to R. This shows the path of the ray of light through the block.

Measure the length $a$ of line ET on Fig. 1.1. $a=\text{.................................................... cm}$

Measure the length $b$ of line ER on Fig. 1.1. $b=\text{.................................................... cm}$

On Fig. 1.1, extend the line FE into the block, until it meets the line RT. Label the point where FE meets RT with the letter G. Measure the length $c$ of line EG on Fig. 1.1. $c=\text{.................................................... cm}$

Use your values from (c)(i) and (c)(ii) to calculate a first value $n_1$ for the refractive index of the block. Use the equation shown. $$n_1=\frac{b}{2a}$$ $n_1=\text{.........................................................}$

Use your values from (c)(ii) and (d) to calculate a second value $n_2$ for the refractive index of the block. Use the equation shown. $$n_2=\frac{b}{c}$$ $n_2=\text{.........................................................}$

Two quantities can be considered to be the same within the limits of experimental accuracy if their values are within $10\mathrm{\%}$ of each other. Compare your value $n_1$ for the refractive index calculated in (e)(i) with the value $n_2$ calculated in (e)(ii). State if your two values can be considered to be the same. Support your statement with a calculation. calculation statement ..................................................................................................................................

One source of inaccuracy in this experiment is careless measurement. Suggest another source of inaccuracy in this experiment.

The student measures the room temperature ${\theta }_R$. The thermometer is shown in Fig. 2.2. Record the reading of ${\theta }_R$ on the answer line. ${\theta }_R={\text{..................................................... }}^{\circ }\text{C}$

The student: • closes the switch • records the potential difference across the thermistor $V_{XY}$ while the thermistor is at room temperature ${\theta }_R$ in the top row of Table 2.1 • opens the switch. The voltmeter is shown in Fig. 2.3. Record the potential difference $V_{XY}$ while the thermistor is at room temperature ${\theta }_R$ in Table 2.1.

The student: • disconnects the voltmeter from points X and Y • reconnects the voltmeter across the $220\mathrm{\Omega }$ resistor between points Y and Z • closes the switch and records the potential difference across the $220\mathrm{\Omega }$ resistor $V_{YZ}$ while the thermistor is at room temperature ${\theta }_R$ in the top row of Table 2.1. Re-draw the circuit shown in Fig. 2.1 on page 5 to show the voltmeter connected to measure the potential difference across the $220\mathrm{\Omega }$ resistor.

The student: • pours some hot water into the beaker containing the thermistor • places the thermometer into the hot water and stirs the water gently • waits for $30\text{ s}$ • measures the temperature of the hot water ${\theta }_H$ • measures new values for potential differences $V_{XY}$ and $V_{YZ}$ while the thermistor is at the temperature of the hot water ${\theta }_H$. The temperature of the hot water ${\theta }_H$ is $83{}^{\circ }\text{C}$. The student’s measurements are recorded in the bottom row of Table 2.1. Explain why the student waits for $30\text{ s}$ before measuring the temperature of the hot water.

Explain why the student stirs the water before reading the temperature of the hot water from the thermometer.

Examine the data in Table 2.1. Compare the reading for the potential difference across the thermistor $V_{XY}$ at room temperature ${\theta }_R$ with the reading for the potential difference across the thermistor $V_{XY}$ at the temperature of the hot water ${\theta }_H$. Suggest what causes the difference in the readings.

The current $I$ in the circuit is calculated using the equation: $$I=\frac{V_{YZ}}{R}$$ where $R=220\mathrm{\Omega }$. Use the measurements recorded in Table 2.1 to calculate the current $I$ at room temperature ${\theta }_R$ and at the temperature of the hot water ${\theta }_H$. Record your answers in Table 2.1.

The resistance $R_T$ of the thermistor is calculated using the equation: $$R_T=\frac{V_{XY}}{I}$$ Use the data in Table 2.1 on page 6 to calculate $R_T$ at room temperature ${\theta }_R$ and at the temperature of the hot water ${\theta }_H$. $R_T\text{ at room temperature }{\theta }_R=\text{...........................................................}\mathrm{\Omega }$ $R_T\text{ at temperature of hot water }{\theta }_H=\text{...........................................................}\mathrm{\Omega }$

Calculate $\alpha$, the average change in the resistance of the thermistor per degree Celsius, for the thermistor as the temperature of the thermistor rises from room temperature ${\theta }_R$ to the temperature of the hot water ${\theta }_H$. Use the equation shown. $$\alpha =\frac{\text{change in resistance of thermistor}}{\text{change in temperature}}$$ Give your answer to 2 significant figures. $\alpha =\text{................................................ }\mathrm{\Omega }\mathrm{/}{}^{\circ }\text{C}$

The student takes readings from the metre rule to determine the length of the spring. On Fig. 3.2, take readings from the metre rule level with the top of the spring and level with the bottom of the spring. Do not include the loops at the top and the bottom of the spring in your measurements. Record your readings to the nearest $0.1\text{ cm}$. reading level with top of spring = .......................................................... cm reading level with bottom of spring = .......................................................... cm

Draw on Fig. 3.2 to show how the student uses a set-square to take a reading from the metre rule level with the bottom of the spring.

Calculate the length $l$ of the coiled part of the spring. Use the equation shown. $$l=\text{reading level with bottom of spring}-\text{reading level with top of spring}$$ Show your working. Record $l$ in Table 3.1 on page 12 for a load $L=0.0\text{ N}$.

The student: • places a load $L=1.0\text{ N}$ on the spring • takes readings to determine the new length $l$ of the spring. The top of the spring does not move but the bottom of the spring moves downwards. The student determines that the new reading on the rule level with the bottom of spring is $45.2\text{ cm}$. Calculate the new length $l$ of the spring. Record your answer for the new length $l$ for a load $L=1.0\text{ N}$ in Table 3.1 on page 12.

The student repeats the procedure in (b)(ii) for loads $L=2.0\text{ N}$, $3.0\text{ N}$, $4.0\text{ N}$ and $5.0\text{ N}$. The results are shown in Table 3.1. Table 3.1 On the grid provided in Fig. 3.3 on page 13, plot a graph of $l$ on the y-axis against $L$ on the x-axis. Start from the origin (0, 0). Draw the straight line of best fit.

Use the data in Table 3.1 and the graph in Fig. 3.3 to determine the extension of the spring when a load of $3.5\text{ N}$ is added to the spring. Show your working. extension = .................................................... cm

A student suggests that the stretched length $l$ of the spring is proportional to load $L$. State if the data in Table 3.1 supports this suggestion. Justify your statement using the data in Table 3.1 or the graph in Fig. 3.3. statement .................................................................................................................................. justification ................................................................................................................................

Line of sight (parallax) errors can occur when readings are taken from the metre rule. State one practical technique, other than using a set square, that ensures accurate readings are taken from a metre rule.

The student repeats the procedure described in (c) two more times and averages the readings before calculating the spring lengths $l$ for each load $L$. Explain why the student does this.