New Cartesian Sign Convention - UNSOLVED PRACTICE SET

Q7. State all the rules of the New Cartesian Sign Convention for spherical mirrors. Draw a diagram to illustrate the positive and negative directions.

Q8. An object is placed 30 cm in front of a concave mirror. Write the object distance with correct sign. If the focal length is 15 cm, write f with correct sign.

Q9. What is the sign of magnification for:
(a) a real, inverted image, and
(b) a virtual, erect image? Explain why the signs differ.

Q10. Using sign convention, explain why the focal length of a concave mirror is negative and that of a convex mirror is positive.

Q11. A student solves a mirror problem and gets v = +20 cm. What does the positive sign of v tell us about the nature and position of the image?

Q12. In what situation would the magnification m be:
(a) equal to −1,
(b) greater than +1,
(c) between 0 and +1? Describe each scenario.

Q13. Explain the New Cartesian Sign Convention for mirrors in detail. Your answer must cover:
(a) the origin (pole) and the positive and negative directions for measuring distances,
(b) the signs of u, v, and f for a concave mirror with a real image,
(c) the signs of u, v, and f for a convex mirror with any image,
(d) the sign convention for image height and object height, and
(e) how the sign of magnification tells you whether the image is erect or inverted.

Q14. A student is confused about sign convention and solves a concave mirror problem getting v = +45 cm and m = −3. Help this student by:
(a) identifying what each sign tells us about the image,
(b) explaining the error: how can a real image from a concave mirror have a positive v?
(c) re-solving the problem correctly with u = −15 cm and f = −20 cm,
(d) interpreting the new answer fully, and
(e) providing a checklist of sign errors students commonly make in mirror problems.

Q15. Create a summary table of sign conventions for all four mirror/image scenarios:
(a) concave mirror — real image,
(b) concave mirror — virtual image,
(c) convex mirror — virtual image (only case), and
(d) plane mirror — virtual image. For each scenario fill in the signs of: u, v, f, m. Then use one numerical example for each case to verify the signs using the mirror formula. 

Q16. Apply sign convention and solve: An object is 40 cm in front of a concave mirror with R = 30 cm.
(a) Write u and f with signs.
(b) Calculate v.
(c) Calculate m.
(d) Is the image real or virtual, erect or inverted?
(e) Write a sentence describing the full image characteristics. 

Q17. A convex mirror has focal length +25 cm. An object is placed 50 cm in front of the mirror. 

(a) Write u, f with signs.
(b) Find v.
(c) Find m.
(d) An object 8 cm tall — find the image height and state whether it is erect or inverted.

Q18. In three separate experiments, the following image distances were obtained from mirror problems:
i) v = −60 cm,
(ii) v = +40 cm,
(iii) v → ∞ (infinity).
For each:
(a) state what the sign or value of v tells you about the image,
(b) identify whether the mirror could be concave or convex, and
(c) state one condition (object position) that produces each result.