Lens Formula and Lens Makers Equation - UNSOLVED PRACTICE SET
Chapter: Ray Optics and Optical Instruments | Topic: Lens Formula and Lens Makers Equation
LENS FORMULA AND LENS MAKERS EQUATION - UNSOLVED PRACTICE SET
Topic: Lens Formula and Lens Makers Equation
Multiple Choice Questions
Q1. The lens formula is:
- 1/f = 1/v + 1/u
- 1/f = 1/v − 1/u
- f = v + u
- f = v − u
Q2. The lens maker's formula for a thin lens is:
- 1/f = (n − 1)(1/R₁ − 1/R₂)
- 1/f = (n + 1)(1/R₁ + 1/R₂)
- 1/f = n(1/R₁ − 1/R₂)
- 1/f = (n − 1)(R₁ − R₂)
Q3. For a convex lens, the focal length is:
- Always negative
- Always positive
- Zero
- Infinity
Q4. A biconvex lens has radii of curvature R₁ and R₂. If R₁ = R₂ = R, the focal length is:
- f = R/(2(n−1))
- f = R/(n−1)
- f = 2R/(n−1)
- f = (n−1)/R
Q5. When an object is placed at 2F of a convex lens, the image is formed:
- At F, real and magnified
- At 2F, real and same size
- Between F and 2F, real and diminished
- At infinity
Q6. For a concave lens, the image of a real object is always:
- Real and magnified
- Virtual, erect, and diminished
- Real and diminished
- Virtual and magnified
Short Answer Questions
Q7. State the lens formula and explain the sign convention used for a thin lens.
Q8. What is the lens maker's formula? Explain the meaning of each term.
Q9. Why does a convex lens converge parallel rays of light, while a concave lens diverges them? Explain with a ray diagram.
Q10. An object is placed at the focus of a convex lens. Where is the image formed? Describe its nature.n here...
Q11. A lens has a focal length of −20 cm. Is it convex or concave? Justify your answer.
Q12. How does the focal length of a lens change when it is immersed in water? Explain.
SECTION NAME
Q13. Derive the lens formula (1/f = 1/v − 1/u) for a convex lens when the object is placed beyond 2F. Use a ray diagram and appropriate geometry.
Q14. Derive the lens maker's formula for a thin convex lens. Explain how the radii of curvature and refractive index affect the focal length.
Q15. Using the lens maker's formula, explain how the focal length of a lens depends on:
(a) The refractive index of the lens material
(b) The radii of curvature of the two surfaces
(c) The surrounding medium
Numerical & Application-Based Problems
Q16. A convex lens has a focal length of 20 cm. An object of height 4 cm is placed at a distance of 30 cm from the lens.
(a) Calculate the image distance.
(b) Calculate the magnification.
(c) Determine the height and nature of the image.
(d) Draw a ray diagram to illustrate the image formation.
Q17. A biconvex lens has radii of curvature 20 cm and 30 cm. The refractive index of the glass is 1.5.
(a) Calculate the focal length of the lens in air.
(b) Calculate the focal length when the lens is immersed in water (refractive index 4/3).
(c) Determine whether the lens behaves as converging or diverging in water.
Q18. In your school's physics lab, a student is given a convex lens and asked to determine its focal length using the lens formula.
(a) She places an object at 40 cm from the lens and obtains a sharp image on a screen at 40 cm on the other side. Calculate the focal length.
(b) She then moves the object to 30 cm and finds the image at 60 cm. Verify the lens formula for this case.
(c) The student measures the radii of curvature of the lens surfaces as 20 cm and 30 cm. Using the lens maker's formula, calculate the refractive index of the lens material.
(d) A classmate has a concave lens and cannot form a real image on a screen. Explain how she can still determine the focal length of the concave lens experimentally.