The real image produced by a concave mirror is found to be 0.303 times the size of the ob ject.
If the distance from the mirror to the screen on which the image appears is 1.14 m, what is the focal length of the mirror?
Answer in units of m
To find the focal length of the concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f is the focal length
v is the distance of the image from the mirror (in this case, the distance from the mirror to the screen on which the image appears)
u is the distance of the object from the mirror
Given:
The size of the real image (v/u) is 0.303
The distance from the mirror to the screen (v) is 1.14 m
Now, we need to find the value of u, the distance of the object from the mirror. Since the image formed by the concave mirror is real, the distance of the object (u) will be negative.
Using the magnification formula, we have:
(Magnification) = -v / u = 0.303
Solving this equation for u, we get:
-v / u = 0.303
-v = 0.303u
u = -v / 0.303
Substituting the known values, we get:
u = -1.14 m / 0.303
u ≈ -3.762 m
Now that we have the values for u and v, we can substitute them back into the mirror formula to find the focal length (f):
1/f = 1/v - 1/u
1/f = 1/1.14 - 1/-3.762
Simplifying the equation:
1/f = 0.877 - (-0.266)
1/f = 0.877 + 0.266
1/f = 1.143
Now, we can solve for f:
f = 1 / 1.143
f ≈ 0.874 m
Therefore, the focal length of the concave mirror is approximately 0.874 meters.