A mirror produces an image that is located 28.0 cm behind the

mirror, when the object is located 9.90 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.)

The refractive indices of materials A and B have a ratio of

1/f = 1/do+1/do

for convex the answer is negative

for concave the answer is positive

is this correct formla?

The given formula is not correct for finding the focal length of a mirror. The correct formula to find the focal length (f) of a mirror is:

1/f = 1/do + 1/di

where:
- f is the focal length of the mirror,
- do is the object distance (distance of the object from the mirror) in meters,
- di is the image distance (distance of the image from the mirror) in meters.

Now let's solve the problem using the correct formula:

a) Given:
do (object distance) = 9.90 cm = 0.099 meters
di (image distance) = -28.0 cm = -0.28 meters

Using the formula 1/f = 1/do + 1/di, we can substitute the values:
1/f = 1/0.099 + 1/(-0.28)

Now, simplify the equation by finding the least common denominator:
1/f = (-0.28 + 0.099) / (0.099 * -0.28)
1/f = (-0.181) / (-0.02772)
1/f = 6.53

To obtain the focal length (f), we take the reciprocal of both sides:
f = 1/6.53
f ≈ 0.153 meters

Therefore, the focal length of the mirror is approximately 0.153 meters.

b) To determine if the mirror is concave or convex, we can use the sign convention. In this convention, if the focal length is positive, the mirror is concave, and if the focal length is negative, the mirror is convex.

The calculated focal length (f) is positive, so the mirror in this case is concave.

To summarize:
a) The focal length of the mirror is approximately 0.153 meters.
b) The mirror is concave.

The formula you provided is incorrect. The correct formula to calculate the focal length (f) of a mirror is:

1/f = 1/do + 1/di

Where:
- f is the focal length of the mirror,
- do is the object distance (distance from the object to the mirror), and
- di is the image distance (distance from the mirror to the image).

Using the given information that the image is located 28.0 cm behind the mirror when the object is located 9.90 cm in front of the mirror, we can substitute the values into the formula:

1/f = 1/9.90 + 1/-28.0

(a) Solving this equation will give us the value of the focal length (f).

(b) To determine if the mirror is concave or convex, we need to compare the given focal length (from part a) with the sign convention for mirrors. If the focal length is positive, the mirror is convex. If the focal length is negative, the mirror is concave.

Note: The sign convention for mirrors is that a positive focal length indicates concave mirror and a negative focal length indicates convex mirror.