Mirror Formula and Magnification - UNSOLVED PRACTICE SET
Chapter: Ray Optics and Optical Instruments | Topic: Mirror Formula and Magnification
MIRROR FORMULA AND MAGNIFICATION - UNSOLVED PRACTICE SET
Topic: Mirror Formula and Magnification
Multiple Choice Questions
Q1. The mirror formula is:
- 1/f = 1/v + 1/u
- 1/f = 1/v − 1/u
- f = v + u
- f = v − u
Q2. The magnification produced by a spherical mirror is given by:
- m = v/u
- m = −v/u
- m = u/v
- m = f/u
Q3. If the magnification produced by a concave mirror is −2, the image is:
- Virtual and diminished
- Real and magnified
- Virtual and magnified
- Real and diminished
Q4. For a convex mirror, the magnification is always:
- Positive and less than 1
- Negative and greater than 1
- Positive and greater than 1
- Negative and less than 1
Q5. An object is placed at a distance of 2f from a concave mirror. The magnification is:
- +1
- −1
- +2
- −2
Q6. If the image formed by a spherical mirror is virtual, the magnification is:
- Always negative
- Always positive
- Zero
- Infinity
Short Answer Questions
Q7. Write the mirror formula and explain the meaning of each term with proper sign convention.
Q8. Define linear magnification for a spherical mirror. What does the sign of magnification indicate about the nature of the image?
Q9. An object is placed at the centre of curvature of a concave mirror. What is the magnification? Describe the image.
Q10. Why is the focal length of a convex mirror taken as negative in the Cartesian sign convention?
Q11. A concave mirror produces a magnification of +3. Where is the object placed relative to the mirror?
Q12. How can you determine the focal length of a concave mirror experimentally using the mirror formula?
Long Answer Questions
Q13. Derive the mirror formula (1/f = 1/v + 1/u) for a concave mirror when the object is placed beyond the centre of curvature. Use a ray diagram and appropriate geometry.
Q14. Derive the expression for linear magnification (m = −v/u = f/(f−u) = (f−v)/f) for a spherical mirror. Show how the sign of magnification determines the nature of the image.
Q15. Using the mirror formula, analyze the image formation by a concave mirror for different object positions. Show mathematically how the nature, position, and size of the image change as the object moves from infinity to the pole.
Numerical & Application-Based Problems
Q16. A concave mirror has a focal length of 20 cm. An object is placed at a distance of 30 cm from the mirror.
(a) Calculate the image distance.
(b) Calculate the magnification.
(c) Determine the nature and size of the image.
(d) If the object is moved 10 cm closer to the mirror, find the new position and nature of the image.
Q17. A convex mirror of focal length 15 cm forms an image that is half the size of the object.
(a) Calculate the object distance.
(b) Calculate the image distance.
(c) If the object is moved 10 cm towards the mirror, calculate the new magnification.
(d) Describe how the image changes as the object approaches the mirror.
Q18. In your school's physics lab, a student is given a concave mirror and asked to determine its focal length. She places an object at various distances and records the following data:
Table
u (cm) v (cm)
−30 −60
−40 −40
−25 −100
(a) Verify the mirror formula for each set of readings.
(b) Calculate the focal length from each set and find the average value.
(c) For the second reading (u = −40 cm, v = −40 cm), explain the special significance of this position.
(d) The student wants to produce an image that is three times the size of the object. Calculate the two possible object positions for this magnification and describe the nature of the image in each case.