Mirror Formula and Magnification - UNSOLVED PRACTICE SET

Q7. Write the mirror formula and define each symbol. State the sign convention used for distances in mirror problems.

Q8. Define magnification for a mirror. Write two expressions for it (one in terms of image/object height, one in terms of v and u). What does a negative magnification indicate?

Q9. An object is placed 20 cm in front of a concave mirror of focal length 10 cm. Find the image distance using the mirror formula. State the sign convention you are using.

Q10. For a concave mirror, an object is placed 30 cm in front of it and the image forms 15 cm in front of the mirror. Calculate the focal length and magnification.

Q11. A convex mirror of focal length 15 cm forms an image at 10 cm behind the mirror. Using the mirror formula, find the object distance.

Q12. Explain using the mirror formula why the image formed by a concave mirror is at infinity when the object is at the focus. What happens as the object moves slightly beyond the focus?

Q13. Explain the mirror formula (1/v + 1/u = 1/f) and the concept of magnification in detail. Your answer must cover:
(a) stating the formula and defining each term,
(b) applying New Cartesian Sign Convention — why all distances are measured from the pole,
(c) working through a full numerical example: object at 25 cm from a concave mirror of f = 15 cm — find v and m,
(d) interpreting the sign of m to determine whether the image is erect or inverted, and
(e) the physical meaning when m > 1, m < 1, and m = 1.

Q14. Using the mirror formula, analyse image formation by a concave mirror of focal length 20 cm for an object placed at:
(a) u = –60 cm,
(b) u = –40 cm (at C),
(c) u = –30 cm,
(d) u = –20 cm (at F).
For each case, calculate v, m, and describe the image. Present your results in a table with columns: u, v, m, image nature.

Q15. A torch uses a concave mirror of focal length 2 cm to project a strong beam of parallel light.
(a) Where must the bulb filament be placed? Use the mirror formula to verify.
(b) A doctor uses a concave mirror of focal length 15 cm to focus light on a patient's ear. Where should she hold the mirror for the light source 60 cm away to produce a focused parallel beam?
(c) The same doctor's mirror produces a 3× magnified image. Calculate the object distance and image distance.
(d) What sign does m have in case (c) and what does this tell you about the image?

Q16. A concave mirror has f = −25 cm. An object is placed at u = −75 cm.
(a) Find v using the mirror formula.
(b) Find magnification m.
(c) Describe the image fully (real/virtual, erect/inverted, magnified/same/diminished).
(d) Verify using magnification: if the object is 4 cm tall, find the image height.

Q17. A convex mirror of focal length +30 cm has an object at u = −45 cm.
(a) Find v using the mirror formula.
(b) Find m.
(c) An object 5 cm tall — find the image height.
(d) Is the image real or virtual? How do you know from the sign of v?

Q18. An object is moved from u = −10 cm to u = −40 cm in front of a concave mirror of f = −20 cm. For both positions:
(a) Calculate image distance v.
(b) Calculate magnification m.
(c) Describe the change in image nature as the object moves from inside to outside the focal length.
(d) At what object distance does the mirror produce an image of the same size as the object?