A convex mirror with focal length of -20 cm forms an image 12 cm behind the surface. Where is the object located as measured from the surface?
To determine the location of the object, we can use the mirror formula for a convex mirror:
1/f = 1/v - 1/u
where:
f is the focal length,
v is the distance of the image from the mirror, and
u is the distance of the object from the mirror.
Given:
f = -20 cm (negative sign indicates a concave mirror),
v = 12 cm (Since the image is formed behind the mirror, it has a positive value),
Let's substitute the given values into the formula and solve for u:
1/f = 1/v - 1/u
1/-20 = 1/12 - 1/u
Now, let's simplify the equation:
-1/20 = 1/12 - 1/u
To further simplify the equation, let's find a common denominator:
-3/60 = 5/60 - 1/u
Next, combine the fractions:
-3/60 = (5-1)/60 - 1/u
-3/60 = 4/60 - 1/u
Now, since the denominators are the same:
-3 = 4 - (1/u)
To isolate 1/u, rearrange the equation:
1/u = 4 + 3
1/u = 7
Now, solve for u by taking the reciprocal of both sides:
u = 1/7
Therefore, the object is located 1/7 cm or approximately 0.14 cm from the surface of the convex mirror.