Physics entrance exam, 2014 E.C. (2022)

Two light sources are coherent when they give out the same type of wave, with the same frequency and wavelength, and keep a constant phase difference between them. Only coherent sources can produce a steady, sustained interference pattern.

Check each choice. A is a correct description: coherent waves share one frequency and one wavelength. B is correct: the two waves must be the same type of wave. D is also correct: keeping a constant phase relationship is exactly what allows sustained interference. C is the false statement. If the phase difference keeps changing, the bright and dark positions shift all the time, so no sustained pattern can form.

The question asks for the statement that does NOT describe coherent light, so the answer is C.

Textbook: Physics Grade 10, Unit 6 Electromagnetic wave and geometrical optics, section 6.3 Light as a wave (page 161).

At a junction in a circuit, charge cannot pile up or disappear. Whatever charge flows into the junction each second must flow out in that same second. Kirchhoff's junction rule says the sum of currents entering a junction equals the sum of currents leaving it, and that is conservation of electric charge written for a circuit. The answer is B.

Conservation of energy is the basis of Kirchhoff's other rule, the loop rule, so option A points at the wrong rule.

Textbook: Physics Grade 11, Unit 6 Electrostatics and Electric Circuit.

In the photoelectric effect, light of frequency \(f\) arrives as photons, each carrying energy \(E = hf\). One photon can free one electron from the metal. The maximum kinetic energy of that electron is \(KE_{max} = hf - \phi\), where \(\phi\) is the work function of the metal. So a higher photon energy gives more energetic photoelectrons, which is what option D says.

Why the others fail. A: intensity changes only the number of electrons emitted, never their energy. B: electron energy rises with frequency, and frequency is inversely related to wavelength, so energy is not proportional to wavelength. C: photons with energy below the work function release no electrons at all, however many arrive.

Use the mirror equation \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\) with object distance \(d_o = 25.0\) cm and focal length \(f = 10.0\) cm.

\(\frac{1}{d_i} = \frac{1}{10} - \frac{1}{25} = \frac{5 - 2}{50} = \frac{3}{50}\), so the image distance is \(d_i = \frac{50}{3} \approx 16.7\) cm.

The magnification is \(m = -\frac{d_i}{d_o} = -\frac{16.7}{25.0} \approx -0.67\). The minus sign only tells us the image is inverted; its size is 0.67 times the object, option C.

Option B is the image distance in cm, not the magnification, which is the tempting slip here.

Textbook: Physics Grade 10, Unit 6 Electromagnetic wave and geometrical optics, section 6.5 Mirrors and Lenses (page 174).

A systematic error shifts every reading the same way. A wrongly zeroed scale, for example, makes all readings too high or all too low, so the measured values sit on one side of the true value. A random error changes unpredictably from reading to reading, so the values scatter, sometimes above and sometimes below the true value. That is exactly what option B states.

Option A swaps the cures: averaging many readings reduces random error, and it cannot remove a systematic error because the same bias sits in every reading. Options C and D both swap the two definitions, so they are wrong.

Textbook: Physics Grade 9, Unit 2 Physical Quantities.

Two vectors are collinear when they lie along the same line. That happens when one is a scalar multiple of the other, so their components keep one common ratio.

Test option C: multiply \(2\vec{i} + 3\vec{j}\) by \(-2\) and you get exactly \(-4\vec{i} - 6\vec{j}\). The component ratios agree: \(\frac{-4}{2} = \frac{-6}{3} = -2\). So this pair is collinear (parallel, pointing in opposite directions).

The other pairs fail the ratio test. In option A, for example, \(\frac{-4}{2} = -2\) but \(\frac{6}{3} = +2\), so those two vectors point along different lines.

Textbook: Physics Grade 11, Unit 2 Vectors, section 2.1 Vectors and Types of Vectors (page 17).