use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f.
Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f
Answer:
To prove that an object placed between the focal point (f) and twice the focal point (2f) of a concave mirror produces a real image beyond 2f, we can use the mirror equation:
The mirror equation is given as:
1/f = 1/do + 1/di
Where:
f = focal length of the concave mirror
do = object distance
di = image distance
Given that the object is placed between f and 2f, we have:
f < do < 2f
For a concave mirror, the focal length (f) is negative. Since the object is between f and 2f, the object distance (do) will be negative.
Let’s assume the object distance (do) = -x (where x is a positive value since the object is placed in front of the mirror).
We also know that from the mirror equation:
1/di = 1/f - 1/do
Substitute the values:
1/di = 1/(-f) - 1/(-x)
1/di = -1/f + 1/x
1/di = -1/f + 1/(do)
Since we want to find the image distance when the object is between f and 2f, the image distance is beyond 2f, so di is positive.
Therefore:
1/di = -1/f + 1/(do)
1/di = -1/f + 1/(-x)
1/di = -1/f - 1/x
As the object is placed between f and 2f, the image distance (di) will be greater than 2f. This result proves that placing the object between the focal point and twice the focal point of a concave mirror produces a real image beyond 2f.