A mirror produces an image that is located 50.0 cm behind the mirror, when the object is located 5.50 cm in front of the mirror. (a) What is the focal length of the mirror? (b) Is the mirror 1 - concave or 2 - convex? (Give the number of the correct answer.)
concave
To find the focal length of the mirror, we can use the mirror equation:
1/f = 1/di + 1/do
Where:
- f is the focal length of the mirror,
- di is the image distance (distance of the image from the mirror), and
- do is the object distance (distance of the object from the mirror).
Given:
di = -50.0 cm (The negative sign indicates that the image is formed behind the mirror.)
do = 5.50 cm
Substituting these values into the mirror equation:
1/f = 1/-50.0 + 1/5.50
To solve this equation, we need to find the common denominator:
1/f = -1/50.0 + 1/5.50
1/f = (5.50 - 50.0) / (5.50 * 50.0)
Simplifying the numerator and denominator:
1/f = -44.5 / 275
1/f = -0.1618
So, the focal length of the mirror is approximately -0.1618 cm.
Now, to determine whether the mirror is concave or convex, we can use the sign convention:
If the focal length (f) is positive, the mirror is convex.
If the focal length (f) is negative, the mirror is concave.
Since we obtained a negative focal length (-0.1618 cm), the mirror is concave.
Therefore, the answers are:
(a) The focal length of the mirror is approximately -0.1618 cm.
(b) The mirror is concave.