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

1. In which one of the above cases the mirror will form a diminished image of the object? Justify your answer.     1
2. List two properties of the image formed in case 2.     1
3.   
   1. What is the nature and size of the image formed by mirror C ? Draw ray diagram to justify your answer.     2
      OR
   2. 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.     2

Answer 1

1. In Case 1, where Mirror A has a focal length of 20 cm and an object distance of 45 cm, the mirror will form a diminished image of the object. This is because the object distance (u) is greater than twice the focal length (2f). According to the mirror formula `1/f = 1/u + 1/v`, when u > 2f, the image formed is diminished.

2. The image in Case 2 (Mirror B with a focal length of 15 cm and an object distance of 30 cm) shows two properties:

   1. The image is formed beyond 2f (twice the focal length).
   2. The image is real.
3.    
   1. 1. Nature of the Image: The image will be real, inverted, and formed between the focal point and the mirror's surface.
      2. Size of the Image: When the object distance is less than the focal length but more than half of it, the image will be enlarged.
         
   2. To determine the position of the image created by a concave mirror, use the mirror formula:
      `1/f = 1/u + 1/v`
      Where:
      
      • f is the focal length of the concave mirror,
      • u is the object distance (distance of the object from the mirror),
      • v is the image distance (distance of the image from the mirror).
      • Given: f = −12 cm (negative because it's a concave mirror), u = −18 cm (negative because the object is placed in front of the mirror).
        Substitute the values into the formula:
        v = 36
        The picture is focused 36 cm from the concave mirror's pole. The positive sign indicates that the picture is formed on the same side as the incident light (facing the mirror).