Combination of Lenses - UNSOLVED PRACTICE SET
Chapter: Ray Optics and Optical Instruments | Topic: Combination of Lenses
COMBINATION OF LENSES - UNSOLVED PRACTICE SET
Topic: Combination of Lenses
Multiple Choice Questions
Q1. When two thin lenses of focal lengths f₁ and f₂ are placed in contact, the focal length F of the combination is given by:
- 1/F = 1/f₁ + 1/f₂
- F = f₁ + f₂
- 1/F = 1/f₁ − 1/f₂
- F = f₁ × f₂
Q2. The power of a combination of two lenses in contact is:
- The sum of their individual powers
- The difference of their individual powers
- The product of their individual powers
- The ratio of their individual powers
Q3. Two lenses of powers +4 D and −2 D are placed in contact. The power of the combination is:
- +6 D
- +2 D
- −2 D
- −6 D
Q4. When two lenses are separated by a distance d, the focal length of the combination is given by:
- 1/F = 1/f₁ + 1/f₂
- 1/F = 1/f₁ + 1/f₂ − d/(f₁f₂)
- F = f₁ + f₂ − d
- 1/F = 1/f₁ − 1/f₂ + dion D
Q5. A convex lens and a concave lens of equal focal lengths placed in contact produce:
- A converging system
- A diverging system
- A system with infinite focal length (no focusing)
- A system with zero focal length
Q6. The equivalent focal length of two thin convex lenses in contact is:
- Greater than either focal length
- Less than either focal length
- Equal to the sum of the focal lengths
- Equal to the difference of the focal lengths
Short Answer Questions
Q7. Derive the expression for the focal length of two thin lenses placed in contact.
Q8. Two lenses of powers +5 D and −3 D are placed in contact. Calculate the power and focal length of the combination.
Q9. Why do we use combinations of lenses in optical instruments instead of single lenses?
Q10. Two convex lenses of focal lengths 20 cm and 30 cm are placed coaxially 10 cm apart. Calculate the focal length of the combination.
Q11. What is the advantage of using an achromatic combination of lenses? Explain briefly.
Q12. A convex lens of focal length 15 cm and a concave lens of focal length 10 cm are placed in contact. What is the nature of the combination?
Long Answer Questions
Q13. Derive the expression for the equivalent focal length of two thin lenses separated by a distance d. Show that when d = 0, it reduces to the formula for lenses in contact.
Q14. Explain the formation of an achromatic combination of lenses. Why is it necessary to combine a crown glass convex lens with a flint glass concave lens to eliminate chromatic aberration?
Q15. Discuss the advantages of using combination of lenses in optical instruments. How does combining lenses help in reducing aberrations?
Numerical & Application-Based Problems
Q16. Two thin convex lenses of focal lengths 20 cm and 30 cm are placed coaxially in contact.
(a) Calculate the focal length of the combination.
(b) Calculate the power of the combination.
(c) An object is placed 40 cm from the combination. Find the position of the image.
(d) Determine the magnification produced by the combination.
Q17. A convex lens of focal length 20 cm and a concave lens of focal length 30 cm are placed coaxially 15 cm apart.
(a) Calculate the equivalent focal length of the combination.
(b) Determine whether the combination is converging or diverging.
(c) An object is placed 40 cm in front of the convex lens. Trace the path of rays and find the final image position.
Q18. In your school's physics lab, a student is building a simple telescope using two lenses.
(a) She uses an objective lens of focal length 50 cm and an eyepiece of focal length 5 cm, placed 55 cm apart. Calculate the magnifying power of this telescope when the final image is formed at infinity.
(b) The student then tries to improve the image quality by adding a third lens. She places a convex lens of focal length 20 cm between the objective and eyepiece. Explain how this affects the image quality and aberrations.
(c) A classmate suggests using two identical convex lenses of focal length 10 cm each, placed 20 cm apart, to make a telescope. Calculate the equivalent focal length of this combination and discuss whether this would make a good telescope.
(d) In a compound microscope, the objective has a focal length of 1 cm and the eyepiece has a focal length of 5 cm. The distance between them is 20 cm. Calculate the magnifying power when the final image is formed at the near point (25 cm).