An objects distance is 2m Infront of the convex mirror and the image height is 1/16 times the object height. What is the focal length of the mirror?
We can use the mirror formula to find the focal length of the convex mirror. The mirror formula is given by:
1/f = 1/v - 1/u,
where f is the focal length, v is the image distance, and u is the object distance.
In this case, the object is located 2m in front of the convex mirror, so u = -2m (negative because the object is in front of the mirror). The image height (h') is 1/16 times the object height (h), so h'/h = 1/16.
We can use the magnification formula, h'/h = v/u, to find the image distance:
1/16 = v/-2.
Simplifying, we find:
v = -2/16 = -1/8.
Now, substituting the values into the mirror formula, we have:
1/f = (1/-1/8) - (1/-2).
Simplifying, we find:
1/f = -8 + 4 = -4.
Taking the reciprocal, we find the focal length of the convex mirror:
f = -1/4 = -0.25m.
Therefore, the focal length of the convex mirror is -0.25m.
To find the focal length of a convex mirror, we can use the mirror equation:
1/f = 1/d_o + 1/d_i
Where:
- f is the focal length
- d_o is the object distance
- d_i is the image distance
Given:
- d_o = 2m
- The image height is 1/16 times the object height
Since the image height is smaller than the object height, we can infer that the image is virtual and upright. In this case, the image distance, d_i, will be negative.
We can also use the magnification equation:
m = -d_i / d_o
Where:
- m is the magnification
Given the magnification, we can find the image distance, d_i:
m = -1/16
d_i = m * d_o
d_i = (-1/16) * 2m
d_i = -1/8 m
Now we can substitute the values of d_o and d_i into the mirror equation to find the focal length, f:
1/f = 1/d_o + 1/d_i
1/f = 1/2 + (-1/8)
1/f = 4/8 - 1/8
1/f = 3/8
f = 8/3 m
Therefore, the focal length of the convex mirror is 8/3 meters.