Resolving Power of Optical Instruments - UNSOLVED PRACTICE SET
Chapter: Wave Optics | Topic: Resolving Power of Optical Instruments
RESOLVING POWER OF OPTICAL INSTRUMENTS - UNSOLVED PRACTICE SET
Topic: Resolving Power of Optical Instruments
Multiple Choice Questions
Q1. The resolving power of an optical instrument is its ability to:
- Magnify objects
- Distinguish two closely spaced objects as separate
- Produce bright images
- Focus light accurately
Q2. According to Rayleigh's criterion, two point sources are just resolved when:
- The central maximum of one falls on the central maximum of the other
- The central maximum of one falls on the first minimum of the other
- The first minimum of one falls on the first minimum of the other
- The intensity at the midpoint is zero
Q3. The limit of resolution of a telescope is given by:
- Δθ = 1.22 λ/D
- Δθ = D/(1.22 λ)
- Δθ = λ/D
- Δθ = D/λ
Q4. The resolving power of a microscope is given by:
- RP = 2μ sin θ / λ
- RP = λ / (2μ sin θ)
- RP = 1.22 λ / D
- RP = D / (1.22 λ)
Q5. To increase the resolving power of a telescope, we should:
- Decrease the aperture of the objective
- Increase the aperture of the objective
- Decrease the focal length of the eyepiece
- Increase the wavelength of light used
Q6. The resolving power of a microscope increases when:
- The wavelength of light increases
- The refractive index of the medium decreases
- The aperture angle increases
- The focal length of the objective increases
Short Answer Questions
Q7. Define resolving power of an optical instrument. What is the difference between resolving power and magnifying power?
Q8. State Rayleigh's criterion for resolution. Draw a diagram showing two just-resolved point sources.
Q9. Why does a telescope with a larger aperture have better resolving power?
Q10. Explain why electron microscopes have much higher resolving power than optical microscopes.
Q11. What is the significance of the numerical aperture (NA) of a microscope objective?
Q12. Why do astronomers prefer to observe using blue light rather than red light for high-resolution observations?
Long Answer Questions
Q13. State and explain Rayleigh's criterion for the resolution of two point sources. Derive the expression for the limit of resolution of a telescope.
Q14. Explain the factors that affect the resolving power of a microscope. Derive the expression for its resolving power and discuss how oil immersion improves resolution.
Q15. Compare the resolving powers of:
(a) Human eye
(b) Optical microscope
(c) Electron microscope
Discuss the physical principles that determine the limits of each.
Numerical & Application-Based Problems
Q16. A telescope has an objective of diameter 20 cm. It is used to observe two stars that emit light of wavelength 550 nm.
(a) Calculate the limit of resolution of the telescope.
(b) Calculate the minimum angular separation between the two stars that can be resolved.
(c) If the focal length of the objective is 4 m, calculate the linear separation between the images of the two just-resolved stars in the focal plane.
Q17. An optical microscope uses light of wavelength 500 nm. The numerical aperture of the objective is 0.9.
(a) Calculate the limit of resolution of the microscope in air.
(b) Calculate the resolving power.
(c) If oil immersion is used (refractive index 1.5) with the same numerical aperture, calculate the new limit of resolution.
Q18. In your school's astronomy club, students are comparing different telescopes.
(a) The school has a small telescope with an objective diameter of 5 cm. Calculate its limit of resolution for light of wavelength 500 nm.
(b) The Vainu Bappu Observatory in Tamil Nadu has a telescope with an objective mirror of diameter 2.3 m. Calculate its limit of resolution for the same wavelength.
(c) Compare the resolving powers of these two telescopes. How much better can the large telescope resolve details compared to the small one?
(d) A student suggests that simply increasing the magnification of the small telescope can match the resolving power of the large telescope. Explain why this is not possible and what limits the resolution.
(e) The Hubble Space Telescope has an aperture of 2.4 m. Explain why it can resolve finer details than ground-based telescopes of the same size, despite being in space. What additional advantage does the James Webb Space Telescope (with a 6.5 m mirror) have?