Key Terms - Pole, Centre of Curvature, Focal Length - UNSOLVED PRACTICE SET

Q7. Define the following terms for a spherical mirror:
(a) Pole,
(b) Principal axis,
(c) Aperture. Draw and label a diagram.

Q8. What is the centre of curvature of a spherical mirror? How is it related to the radius of curvature? Where does it lie relative to the mirror?

Q9. Define the principal focus of
(a) a concave mirror and
(b) a convex mirror. Why is the focus of a convex mirror called a 'virtual' focus?

Q10. Derive the relationship f = R/2 for a spherical mirror. (Hint: use a ray parallel to the principal axis and the law of reflection at the point of incidence.)

Q11. A spherical mirror has a radius of curvature of 28 cm.
(a) What is its focal length?
(b) If this is a concave mirror, where is the focus relative to the mirror?

Q12. What is the 'aperture' of a spherical mirror? Why are spherical mirrors with small apertures preferred in optics for getting accurate results?

Q13. Draw (or describe in full detail) a concave mirror and label all the following: Pole (P), Centre of Curvature (C), Principal Focus (F), Principal Axis, Radius of Curvature (R), Focal Length (f), and Aperture. For each labelled part:
(a) give the precise definition,
(b) state its position relative to P, and
(c) state its significance in ray diagrams.

Q14. Explain how the principal focus of a concave mirror is determined experimentally.
(a) Describe the experimental method using sunlight or a distant object.
(b) Explain why parallel rays converge at the focus after reflection.
(c) Why is the focus of a concave mirror 'real' while that of a convex mirror is 'virtual'?
(d) What happens when an object is placed at the focus of a concave mirror — where does the image form?
(e) Give one practical application that exploits the focusing property of a concave mirror.

Q15. Explain the relationship between the radius of curvature (R) and the focal length (f) for spherical mirrors.
(a) State the relationship f = R/2.
(b) Prove this geometrically for a concave mirror using a ray parallel to the principal axis and the law of reflection.
(c) Does this relationship hold exactly for mirrors with large apertures? Explain the concept of spherical aberration briefly.
(d) Calculate f when R = 50 cm, 32 cm, and 15 cm.
(e) If f = 12 cm, what is R?

Q16. A satellite dish is shaped like a concave mirror with a radius of curvature of 2.4 m.
(a) Calculate its focal length.
(b) Parallel signals from a distant satellite arrive and reflect off the dish. Where should the signal receiver be placed?
(c) Why is the concave (paraboloid) shape ideal for a satellite dish?
(d) What would happen if a convex dish were used instead?

Q17. A student sets up a concave mirror experiment. She finds that when a candle is placed 30 cm from the mirror, a sharp image forms at 30 cm on the other side.
(a) At which special point is the image formed — F or C?
(b) Calculate the radius of curvature.
(c) Calculate the focal length.
(d) What is the nature of the image (real/virtual, erect/inverted, magnified/same)?

Q18. Fill in the missing values and answer:
(a) A concave mirror has f = 20 cm. Find R.
(b) A convex mirror has R = 50 cm. Find f.
(c) A concave mirror has f = −15 cm (sign convention). Find R.
(d) An object is placed at C (object distance = R). Using the mirror formula 1/v + 1/u = 1/f, show that the image also forms at C.