Lens Formula and Magnification - UNSOLVED PRACTICE SET
Chapter: Light Reflection and Refraction | Topic: Lens Formula and Magnification
LENS FORMULA AND MAGNIFICATION - UNSOLVED PRACTICE SET
Topic: Lens Formula and Magnification
Multiple Choice Questions
Q1. The lens formula is:
- 1/v + 1/u = 1/f
- 1/v − 1/u = 1/f
- 1/f = 1/v × 1/u
- v − u = f
Q2. The magnification of a lens is defined as:
- m = –v/u
- m = v/u
- m = f/u
- m = v/f
Q3. For a convex lens, when the object is at 2F, the image is:
- At F
- At 2F on the other side
- At infinity
- Between F and optical centre
Q4. If the magnification of a lens is −3, the image is:
- Virtual, erect, 3 times larger
- Real, inverted, 3 times larger
- Virtual, inverted, 3 times smaller
- Real, erect, 3 times larger
Q5. Using the lens formula with u = −20 cm and f = +10 cm (convex lens), v equals:
- −20 cm
- 20 cm
- −10 cm
- 10 cm
Q6. For a concave lens, the image distance v is always:
- Positive
- Negative
- Zero
- Can be positive or negative
Short Answer Questions
Q7. Write the lens formula and explain how it differs from the mirror formula. Define each symbol and state the sign convention.
Q8. Define magnification for a lens. Write both forms of the magnification formula. What does a positive magnification indicate for a lens?
Q9. An object is placed 30 cm from a convex lens of focal length 15 cm. Find the image distance and magnification.
Q10. A concave lens of focal length 20 cm has an object at 40 cm. Find the image position and state whether it is real or virtual.
Q11. A convex lens forms an image twice the size of the object on a screen. If the image is real, find the relationship between object distance and focal length.
Q12. Why does the lens formula give v = ∞ (infinity) when the object is at the principal focus of a convex lens? What does this mean physically?
Long Answer Questions
Q13. Explain the lens formula and magnification for a convex lens in detail. Your answer must cover:
(a) the formula 1/v − 1/u = 1/f,
(b) the New Cartesian Sign Convention for lenses (how it differs from mirrors),
(c) a step-by-step numerical example with u = −40 cm, f = +20 cm,
(d) interpreting the sign of m to find image nature, and
(e) what happens to v and m as u varies from −∞ to just inside F.
Q14. Using the lens formula, systematically calculate image positions for a convex lens (f = +20 cm) with the object at:
(a) u = −60 cm,
(b) u = −40 cm,
(c) u = −30 cm,
(d) u = −20 cm (at F). For each, calculate v and m.
Present in a table: u, v, m, image nature. Then
(e) describe the trend: what happens to the image distance as the object approaches F?
Q15. A slide projector uses a convex lens to project a large image of a small transparent slide onto a distant screen.
(a) If the slide (object) is placed 5 cm from a lens of focal length 4.5 cm, find v and m using the lens formula.
(b) If the screen is 450 cm from the lens, verify using the lens formula what the focal length must be.
(c) The slide is 3 cm × 2 cm — find the image dimensions.
(d) Is the image real or virtual? Erect or inverted?
(e) Why does the slide need to be inserted upside down in a projector?
Numerical / Application-Based Problems
Q16. A convex lens has f = +25 cm. An object 4 cm tall is placed at u = −100 cm.
(a) Find v using the lens formula.
(b) Find m.
(c) Find the image height.
(d) Describe the image (real/virtual, erect/inverted, magnified/diminished).
Q17. A concave lens has f = −30 cm. An object 5 cm tall is at u = −60 cm.
(a) Find v.
(b) Find m.
(c) Find image height.
(d) Compare m for concave vs convex lens for the same u and f magnitude.
(e) Which lens type always gives |m| < 1 and why?
Q18. A camera uses a convex lens of focal length 5 cm. A person 160 cm tall stands 200 cm from the camera lens.
(a) Find the image distance v.
(b) Find the magnification.
(c) Find the image height (size of person on the film/sensor).
(d) Is the image real or virtual?
(e) Why must the film be placed exactly at v for a sharp photograph?