Introduction
When an object is placed in front of a diverging mirror, certain characteristics such as the nature and position of the image can be determined using the mirror formula.
Given Data
- Object distance (u) = -15 cm (object distance is taken as negative in mirror conventions)
- Focal length (f) = -6 cm (focal length for a diverging mirror is also negative)
Mirror Formula
The mirror formula is given by:
1/f = 1/v + 1/u
Where:
- f = focal length
- v = image distance
- u = object distance
Calculation of Image Distance
Substituting the values into the formula:
1/(-6) = 1/v + 1/(-15)
Simplifying this, we get:
1/v = 1/(-6) + 1/15
Finding a common denominator (30):
1/v = (-5/30) + (2/30) = -3/30
Thus,
v = -10 cm
Nature of the Image
- The negative sign indicates that the image is formed on the same side as the object.
- The image is virtual since it cannot be projected on a screen.
- It is upright and diminished in size.
Position of the Image
- The image is located at a distance of 10 cm from the mirror, on the same side as the object.
Conclusion
To summarize, when an object is placed 15 cm from a diverging mirror with a focal length of 6 cm, the image formed is virtual, upright, and located 10 cm from the mirror on the same side as the object.