ECAT — Engineering College Admission Test (UET)
Take the ECAT Physics — Physical Optics and Thermodynamics (Set 6): 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 Young's double-slit setup in air (λ = 600 nm, slit separation 0.30 mm, screen 1.5 m away) the fringe width is 3.0 mm. If the entire apparatus is immersed in water (refractive index 4/3), the fringe width becomes
Answer: C. 2.25 mm
Explanation: In water λ' = λ/n, so β' = 3.0/(4/3) = 2.25 mm.
Q2. A thin glass sheet of thickness 12 μm and refractive index 1.5 is placed over one slit of a double-slit apparatus lit by 600 nm light. The central fringe shifts by how many fringe widths?
Answer: D. 10
Explanation: Extra optical path = (n − 1)t = 6 μm = 6×10⁻⁶/6×10⁻⁷ = 10 wavelengths, so the pattern shifts 10 fringes.
Q3. Light passes through a single slit whose width is exactly twice its wavelength. The angle of the first minimum from the central axis is
Answer: A. 30 °
Explanation: a sinθ = λ with a = 2λ gives sinθ = ½, so θ = 30°.
Q4. A diffraction grating has 5000 lines per centimetre and is illuminated normally with 600 nm light. The highest order of principal maximum that can be observed is
Answer: D. 3
Explanation: d = 2.0 μm; n ≤ d/λ = 3.33, and the order must be a whole number, so n = 3.
Q5. A non-reflective coating of refractive index 1.25 is applied to glass of index 1.50 to suppress reflection of 550 nm light at normal incidence. The minimum coating thickness is
Answer: C. 110 nm
Explanation: Both reflections undergo a half-cycle phase change, so cancellation needs 2nt = λ/2: t = λ/4n = 550/5 = 110 nm.
Take the timed test (free, no sign-up) to see your score and the answer and explanation for every question.
Q6. In a Newton's rings experiment the diameter of the 4th dark ring is 4.0 mm. Using Dₙ ∝ √n, the diameter of the 16th dark ring is
Q7. Unpolarized light of intensity I₀ passes through three ideal polarizers whose transmission axes are at 0°, 45° and 90° to the first. The transmitted intensity as a fraction of I₀ is
Q8. In a Michelson interferometer using light of wavelength 500 nm, one mirror is displaced by 0.050 mm. The number of fringes that cross the field of view is
Q9. X-rays are Bragg-reflected from crystal planes spaced 0.25 nm apart. The longest wavelength that can give a Bragg reflection from these planes is
Q10. Two moles of an ideal gas at 300 K expand isothermally to double their volume. Use R = 8.3 J/mol K and ln 2 = 0.7. The heat absorbed by the gas is
Q11. A gas absorbs 500 J of heat while expanding at a constant pressure of 1.0×10⁵ Pa from 2.0 litres to 3.0 litres. The increase in its internal energy is
Q12. A monatomic ideal gas (γ = 5/3) initially at 1.0×10⁵ Pa is compressed adiabatically and reversibly until its volume is one-eighth of the initial value. The final pressure is
Q13. Two moles of a diatomic ideal gas (C_V = 5R/2) are heated by 20 K at constant pressure, with R = 8.31 J/mol K. The heat supplied is
Q14. A Carnot engine works between 500 K and 300 K. The sink temperature is lowered (source unchanged) to raise the efficiency from 40% to 50%. The new sink temperature is
Q15. An ideal (Carnot) refrigerator keeps its interior at 270 K in a room at 300 K. The work needed to remove 1800 J of heat from the interior is
Q16. 0.010 kg of ice at 273 K melts to water at 273 K (latent heat 3.34×10⁵ J/kg). The entropy change of the ice is
Q17. The r.m.s. speed of hydrogen molecules (molar mass 2 g/mol) at 27 °C is equalled by oxygen molecules (molar mass 32 g/mol) at a temperature of
Q18. A gas of density 1.2 kg/m³ has molecules with r.m.s. speed 500 m/s. Using P = ⅓ρ⟨v²⟩, its pressure is
Q19. An air bubble rises isothermally from the bottom of a lake 20 m deep to the surface. Take atmospheric pressure as equivalent to 10 m of water. The ratio of its final volume to its initial volume is
Q20. A gas has molar specific heat at constant volume C_V = 3R (a non-linear polyatomic molecule at high temperature). The ratio γ = C_P/C_V for this gas is
Q21. A gas undergoes a cycle that is a triangle on a P–V diagram, with a pressure range of 2.0×10⁵ Pa and a volume range of 3.0×10⁻³ m³ (base × height). The net work done per cycle is
Q22. Which statement is a correct expression of the Kelvin–Planck form of the second law?
Q23. Two coherent in-phase sources emit waves of wavelength 0.60 m. A point P is 4.5 m from one source and 5.4 m from the other. At P there is
Q24. Light of wavelength 600 nm in air enters glass in which its speed is 2.0×10⁸ m/s (c = 3.0×10⁸ m/s). Its wavelength in the glass is
Q25. A grating with 6000 lines per centimetre gives a second-order maximum at an angle whose sine is 0.60. The wavelength of the light, to three significant figures, is
Q26. A heat engine absorbs 800 J and rejects 600 J in each cycle and completes 10 cycles per second. Its power output is
Q27. Two moles of an ideal gas are heated through 50 K at constant pressure (R = 8.31 J/mol K). The work done by the gas is
Q28. An ideal gas expands freely into a vacuum inside a rigid, thermally insulated container. Which statement is correct for the gas?
Q29. Monochromatic light of wavelength 600 nm falls normally on a thin air wedge of angle 3.0×10⁻⁴ rad. Using fringe spacing β = λ/(2θ), the spacing between adjacent dark fringes is
Q30. Light travelling in water (n = 4/3) is reflected from a glass plate (n = 1.5) and the reflected beam is completely plane-polarized. Using tan θ = n₂/n₁, the angle of incidence is