A-Level Physics: Required Practicals and Uncertainties
A-level Physics required practicals and uncertainties is the practical-skills strand AQA examines directly in the written papers, worth a substantial share of the overall marks, even though no single required practical is assessed as a written lab report. It covers what several of the required practicals actually investigate: determining the acceleration due to gravity, g, by a free-fall method; determining the refractive index and critical angle of a glass or Perspex block; and determining the wavelength of light using two-source (Young's double-slit) interference or a diffraction grating. On top of naming apparatus and technique, the exam questions test identifying independent, dependent and control variables, combining uncertainties correctly, and explaining why a specific measurement technique, such as measuring across several repeats of a small quantity, reduces percentage uncertainty.
Before you start
Make sure you're comfortable with these topics first:
Method
- For the free-fall determination of g, use h = (1/2) x g x t^2, rearranged to g = 2h / t^2, where h is the constant, pre-measured height fallen and t is the time of fall, found electronically using a trapdoor release mechanism connected to a timer and a light gate at the bottom; repeat the timing several times at the same height and use the mean time in the calculation.
- Combine uncertainties correctly for a calculation like g = 2h/t^2: percentage uncertainties are added for quantities that are multiplied or divided, and a percentage uncertainty is multiplied by the power for a quantity raised to a power, so percentage uncertainty in g = percentage uncertainty in h + (2 x percentage uncertainty in t), since t is squared.
- For the refractive index of a glass or Perspex block, measure the angle of incidence in air, theta1, and the angle of refraction in the glass, theta2, for a ray passing from air into the glass, then use n = sin(theta1) / sin(theta2); repeat for several different angles of incidence and plot sin(theta1) against sin(theta2) to find n from the gradient of the resulting straight line, which averages out random error better than a single pair of angle readings.
- Use sin(C) = 1/n to calculate the critical angle, C, of a glass or Perspex block from its refractive index, n, remembering the critical angle only applies to a ray travelling from the more optically dense medium (the glass) towards a less dense medium (air), and that total internal reflection occurs for any angle of incidence inside the glass greater than C.
- For two-source (Young's double-slit) interference, use fringe spacing w = (wavelength x D) / s, where D is the distance from the slits to the screen and s is the slit separation; because a single fringe is very narrow, measure the total width across several fringes, for example ten fringe widths, with a ruler or travelling microscope, then divide by the number of fringes to find the mean fringe spacing, since the same absolute ruler uncertainty then applies to a much larger measured length, greatly reducing the percentage uncertainty in the result.
- For a diffraction grating, use n x wavelength = d x sin(theta), where d is the grating spacing, found from the number of lines per metre stated on the grating (d = 1 / (lines per metre)), n is the order of the maximum observed, and theta is the angle between the straight-through direction and that order's maximum; a diffraction grating produces sharper, more widely spaced maxima than a double slit, allowing wavelength to be measured more precisely.
- Before starting any required practical, identify the independent variable (the one factor deliberately changed), the dependent variable (the one measured as a result), and the control variables (factors kept constant for a fair test), and state these explicitly and precisely rather than as a vague list, since 'identify the variables' questions are marked on precision.
Worked example
A student determines the acceleration due to gravity, g, using a steel ball bearing released from rest by an electromagnet, falling a measured height of h = 1.500 m (measured with a metre ruler of resolution 1 mm) before triggering a light gate connected to an electronic timer. The fall is timed five times, giving: 0.552 s, 0.548 s, 0.556 s, 0.550 s, 0.554 s. (a) Calculate the mean time of fall and use it to calculate g, using h = (1/2) x g x t^2. (b) Calculate the percentage uncertainty in g, given that the percentage uncertainty in h is 0.033%, and using the range of the repeated time readings to find the percentage uncertainty in t.
- Calculate the mean time: (0.552 + 0.548 + 0.556 + 0.550 + 0.554) / 5 = 2.760 / 5 = 0.5520 s.
- Rearrange h = (1/2) x g x t^2 to make g the subject: g = 2h / t^2. Substitute: g = (2 x 1.500) / (0.5520)^2 = 3.000 / 0.304704.
- (a) Final answer: g = 9.85 m/s^2 (3 s.f.).
- (b) Find the absolute uncertainty in t from the spread of repeats: half the range = (0.556 - 0.548) / 2 = 0.004 s. Percentage uncertainty in t = (0.004 / 0.5520) x 100 = 0.725% (3 s.f.).
- Since g = 2h / t^2, combine percentage uncertainties by adding the percentage uncertainty in h to twice the percentage uncertainty in t, because t is squared: percentage uncertainty in g = 0.033% + (2 x 0.725%) = 1.48% (3 s.f.).
- (b) Final answer: percentage uncertainty in g = 1.48%, giving an absolute uncertainty of about 0.15 m/s^2 (1.48% of 9.85). This range, 9.85 +/- 0.15 m/s^2, comfortably includes the accepted value of g, so the result is consistent despite a small systematic effect, such as air resistance or a slight delay in the light gate triggering, that may account for the difference between the mean and the accepted value.
Practice questions
Try each question, then tap to reveal the answer.
Q1In the free-fall determination of g, name the independent variable, the dependent variable, and one variable that should be controlled.Show answer
Answer: Independent variable: the height, h, through which the ball falls (if height is varied to plot a graph). Dependent variable: the time of fall, t. Control variable: the same ball bearing (same mass and size) used for every measurement, so air resistance affects each fall equally.
Q2State why a light gate and electronic timer give a more precise measurement of the time of fall than a student using a stopwatch and their own reaction time.Show answer
Answer: A light gate and electronic timer start and stop automatically at the instant the ball passes a fixed point, removing human reaction time, which is variable and typically around 0.2 s, as a source of uncertainty in the timing.
Q3Light of wavelength 550 nm passes through a diffraction grating with 400 lines per mm. Calculate the grating spacing, d, in metres.Show answer
Answer: d = 1 / (lines per metre) = 1 / (400 x 1000) = 2.5 x 10^-6 m.
Q4A ray of light travelling from air into a glass block has an angle of incidence of 50.0 degrees and an angle of refraction of 30.0 degrees inside the glass. Calculate the refractive index of the glass.Show answer
Answer: n = sin(50.0 degrees) / sin(30.0 degrees) = 0.766 / 0.500 = 1.53 (3 s.f.).
Q5A glass block has a refractive index of 1.55. Calculate its critical angle.Show answer
Answer: sin(C) = 1/n = 1/1.55 = 0.645. C = sin^-1(0.645) = 40.2 degrees (3 s.f.).
Q6State why total internal reflection can only occur when light travels from a more optically dense medium towards a less optically dense medium, for example from glass towards air, and not the other way round.Show answer
Answer: Total internal reflection requires the refracted ray to bend away from the normal enough to reach 90 degrees (grazing emergence) at the critical angle; light travelling from a less dense to a more dense medium bends towards the normal on refraction, so it can never reach or exceed 90 degrees, and total internal reflection cannot occur in that direction.
Q7Explain why, in a double-slit interference experiment, a student measures the distance across ten fringe widths rather than measuring a single fringe width directly.Show answer
Answer: The ruler's absolute uncertainty is fixed by its resolution regardless of what is measured, so applying it to a much larger measured distance, ten fringe widths, gives a much smaller percentage uncertainty than applying the same absolute uncertainty to one narrow fringe measured directly; dividing the ten-fringe measurement by ten then gives the mean single fringe width with this same, smaller percentage uncertainty.
Q8A pendulum's period is investigated by timing 20 complete oscillations, rather than a single oscillation, using a stopwatch. Calculate the percentage uncertainty in the period of one oscillation if timing 20 oscillations takes 25.0 s with an absolute uncertainty of 0.4 s.Show answer
Answer: Percentage uncertainty in the time for 20 oscillations = (0.4/25.0) x 100 = 1.6%. Dividing by 20, an exact number, to find the period of one oscillation does not change this percentage uncertainty, so the percentage uncertainty in the period is also 1.6%.
Exam-style questions
Written in the style of a A Level Science exam paper, with a full mark scheme.
A student sets up a double-slit interference experiment using blue light of wavelength 480 nm, with the slits a distance D = 1.50 m from a screen and a slit separation s = 0.20 mm. (a) Calculate the expected fringe spacing, w. (b) The student measures the distance across ten fringe widths as 36.0 mm, using a ruler of resolution 1 mm, so the ten-fringe measurement, from two ruler readings, has an absolute uncertainty of 1.0 mm. Calculate the percentage uncertainty in this ten-fringe measurement. (c) Explain why this percentage uncertainty is much smaller than the percentage uncertainty that would be obtained by measuring a single fringe width directly with the same ruler.
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A student investigates the refractive index of a glass block by measuring the angle of refraction, theta2, in the glass for five different angles of incidence, theta1, in air, then plots a graph of sin(theta1) (y-axis) against sin(theta2) (x-axis). The graph is a straight line through the origin with a gradient of 1.48. (a) Explain how this gradient value is used to find the refractive index of the glass. (b) Suggest one advantage of finding the refractive index from the gradient of a graph using five data points, rather than from a single pair of angle measurements.
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A student investigates how the period, T, of a simple pendulum depends on its length, l, by timing 20 oscillations at each of six different lengths and plotting a graph of T^2 against l. (a) State the independent variable, the dependent variable, and one variable that should be controlled in this investigation. (b) Suggest one reason why the student times 20 oscillations, rather than a single oscillation, at each length. (c) The student's graph does not pass exactly through the origin, but through a point slightly above it on the T^2 axis. Suggest one practical reason for this.
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