Find the distance of the image when an object is placed on the principal axis at a distance of 10 cm. In front of concave mirror whose radius of curvature is 8 cm
To find the distance of the image when an object is placed on the principal axis in front of a concave mirror, you can use the mirror equation:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = distance of the image from the mirror
u = distance of the object from the mirror
In this case, the object is placed on the principal axis at a distance of 10 cm, and the radius of curvature of the mirror is 8 cm.
Since the mirror is concave, the focal length (f) is half the radius of curvature (R):
f = R/2 = 8 cm / 2 = 4 cm
Plugging in the values into the mirror equation:
1/4 = 1/v - 1/10
Now, let's solve this equation to find the distance of the image from the mirror (v):
Multiply both sides by 40v:
10v = 40 - 4v
Add 4v to both sides:
14v = 40
Divide both sides by 14:
v = 40/14
v ≈ 2.857 cm
Therefore, the distance of the image when an object is placed on the principal axis at a distance of 10 cm in front of a concave mirror with a radius of curvature of 8 cm is approximately 2.857 cm.