Question

Study the data given below showing the focal length of three concave mirrors A, B and C and the respective distances of objects placed in front of the mirrors:

Case	Mirror	Focal Length (cm)	Object Distance (cm)
1	A	20	45
2	B	15	30
3	C	30	20

(i) In which one of the above cases the mirror will form a diminished image of the object? Justify your answer.
(ii) List two properties of the image formed in case 2.
(iii) (A) What is the nature and size of the image formed by mirror C? Draw ray diagram to justify your answer.

OR

(iii) (B) An object is placed at a distance of 18 cm from the pole of a concave mirror of focal length 12 cm. Find the position of the image formed in this case.

Answer 1

(i). Case 1 (Mirror A): Object distance (45 cm) is beyond the center of curvature (C = 2f = 40 cm). When the object is beyond C, the image formed is diminished, inverted, and located between f and C.

(ii). List two properties of the image formed in case 2.
Solution: Case 2 (Mirror B): Object distance (30 cm) is at the center of curvature (C = 2f = 30 cm).
Image Properties:
• The image is real and inverted.
• The image is the same size as the object.

(iii)A Case 3 (Mirror C): Object distance (20 cm) is less than the focal length (30 cm).
Image Nature: Virtual, erect, and magnified.
Ray Diagram: A ray originating from the object parallel to the principal axis refracts through the focal point. A ray passing through the center of curvature, its virtual rays appear to meet behind the mirror.

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(ii) Using the mirror formula:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] 
\[ \frac{1}{12} = \frac{1}{v} - \frac{1}{-18} \] 
\[ \frac{1}{v} = \frac{1}{12} + \frac{1}{18} = \frac{3 + 2}{36} = \frac{5}{36} \] 
\[ v = 7.2 \, \text{cm} \, (\text{Image is real and inverted, located at } 7.2 \, \text{cm from the mirror}). \]