an object is placed at a distance of 12 centimetre from a concave mirror of radius of curvature is 16 cm find the position of image
To find the position of the image formed by a concave mirror, we can use the mirror equation:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror,
- v is the image distance (distance of the image from the mirror), and
- u is the object distance (distance of the object from the mirror).
In this case, the radius of curvature (R) is given as 16 cm. The focal length (f) of a concave mirror is half of the radius of curvature, so f = R/2 = 16/2 = 8 cm.
The object distance (u) is given as 12 cm.
Substituting these values into the mirror equation, we get:
1/8 = 1/v - 1/12
To solve for v, we need to rearrange the equation. Adding 1/12 to both sides:
1/8 + 1/12 = 1/v
Multiplying both sides by 24v to get rid of the denominators:
3v + 2v = 24
5v = 24
v = 24/5
Therefore, the image distance (v) is 4.8 cm.
Since the object is placed in front of the concave mirror, the image will be formed on the same side as the object. Thus, the position of the image is 4.8 cm in front of the mirror.