ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Physical Optics and Thermodynamics (Set 7): 30 multiple-choice questions (40 minutes) with instant scoring and a full answer…
What this test covers
The first 5 questions of this test, with the correct answer and explanation.
Q1. In a double-slit experiment the slits are 0.3 mm apart, the screen is 1.5 m away and the light has wavelength 600 nm. The fringe spacing is:
Answer: B. 3 mm
Explanation: β = λD/d = (600 × 10⁻⁹)(1.5)/(0.3 × 10⁻³) = 3 mm.
Q2. A double-slit set-up with a fringe spacing of 3 mm in air is completely immersed in water of refractive index 4/3. The new fringe spacing is:
Answer: C. 2.25 mm
Explanation: Wavelength in water = λ/n, so β′ = β/n = 3/(4/3) = 2.25 mm.
Q3. In a double-slit pattern with fringe spacing 3 mm, the distance on one side of the central fringe between the 2nd dark fringe and the 4th bright fringe is (count the first dark fringe, at β/2, as the 1st):
Answer: D. 7.5 mm
Explanation: 2nd dark is at (1 + ½)β = 1.5β from the centre (counting the first dark as ½β); 4th bright is at 4β. Difference = 2.5β = 7.5 mm.
Q4. White light falls normally on a thin film (n = 1.5) in air. Taking the reflected wave to gain a half-wavelength phase shift at the top surface only, the minimum film thickness giving strong reflection for λ = 600 nm is:
Answer: C. 100 nm
Explanation: Constructive reflection: 2nt = (m + ½)λ; with m = 0, t = λ/4n = 600/6 = 100 nm.
Q5. In a Newton's rings experiment the diameter of the nth dark ring is proportional to √n. The ratio of the diameter of the 16th dark ring to that of the 4th is:
Answer: D. 2
Explanation: D ∝ √n, so D₁₆/D₄ = √(16/4) = 2.
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Q6. A diffraction grating has 5000 lines per cm and is illuminated normally by light of wavelength 600 nm. The highest order of maximum that can be observed is:
Q7. A single slit 0.1 mm wide is illuminated by 500 nm light and the pattern is viewed on a screen 2 m away. The width of the central maximum is:
Q8. Unpolarized light of intensity 80 W/m² passes through a polarizer and then an analyser whose axis is 60° to the polarizer's. The final intensity is:
Q9. Light reflected from glass of refractive index √3 is completely plane-polarized. The angle of incidence is:
Q10. In a Michelson interferometer, moving one mirror through 0.15 mm makes 500 fringes cross the field of view. The wavelength of the light is:
Q11. X-rays of wavelength 0.15 nm reflect from crystal planes 0.3 nm apart. The glancing angle for the second-order Bragg maximum is:
Q12. According to Huygens' principle, a new wavefront is obtained by:
Q13. Two light sources are said to be coherent when:
Q14. A gas absorbs 500 J of heat and does 200 J of work in expanding. Its internal energy:
Q15. A gas at a constant pressure of 2 × 10⁵ Pa expands from 3 litres to 8 litres. The work done by the gas is:
Q16. A gas goes round a rectangular cycle on a P–V diagram, with pressures 1 × 10⁵ Pa and 3 × 10⁵ Pa and volumes 2 L and 5 L. The net work done per cycle is:
Q17. A Carnot engine with its sink at 300 K has an efficiency of 40%. To raise its efficiency to 50% with the sink unchanged, the source temperature must be raised by:
Q18. A body at a constant temperature of 300 K absorbs 600 J of heat reversibly. Its entropy change is:
Q19. At the same temperature, the ratio of the rms speed of hydrogen (molar mass 2 g/mol) to that of oxygen (32 g/mol) is:
Q20. An ideal gas is at 27°C (300 K). Taking 0 K = −273°C, at what Celsius temperature will the rms speed of its molecules be doubled?
Q21. Taking R = 8 J/(mol K), the heat needed to raise the temperature of 2 mol of a monatomic ideal gas by 10 K at constant volume is:
Q22. A gas at 1 atm and 300 K is heated to 600 K while its volume is halved. The final pressure is:
Q23. An ideal gas is compressed rapidly in a perfectly insulated cylinder. Its temperature rises because:
Q24. An ideal refrigerator keeps its inside at 270 K while the room is at 300 K. Its coefficient of performance, Tc/(Th − Tc), is:
Q25. An ideal gas is heated at constant volume and receives 600 J of heat. The work done by the gas and the change in its internal energy are:
Q26. A heat engine takes 500 J from a hot source and rejects 400 J to a cold sink in every cycle, and completes 5 cycles each second. Its power output is:
Q27. A vertical soap film in air is lit by white light. Near the top, where the film becomes much thinner than a wavelength, it looks black in reflected light because:
Q28. In a two-source interference set-up, the sources are in phase. A point at which the path difference is 2.5λ is:
Q29. A grating has 5000 lines per cm. The angle of the second-order maximum for 500 nm light is:
Q30. A gas of density 1.2 kg/m³ has an rms molecular speed of 500 m/s. Using P = ⅓ρ⟨v²⟩, its pressure is: