A spherical concave mirror has a raduis of curvature of 6.0 cm. At what distance from the mirror should a 6.0 cm object be placed to obtain an image that is 48 cm tall?

The distance from the mirror should be 24 cm.

To determine the distance from the mirror where the object should be placed, we can use the mirror formula:

1/f = 1/v - 1/u

Where:
f = focal length of the mirror
v = image distance
u = object distance

Since we have a concave mirror, the focal length is negative:

f = -6.0 cm

We are given the height of the image:

h' = 48 cm

By using the magnification formula, we can relate the height of the object (h) to the height of the image (h'):

h'/h = -v/u

Substituting known values:

48 cm / 6 cm = -v/u

Simplifying:

v/u = -8

Now, we can substitute the value of v/u in the mirror formula:

1/f = 1/v - 1/u

1/(-6.0 cm) = 1/v - 1/u

Simplifying further:

-1/6.0 cm = -1/8 - 1/u

We can combine the fractions:

-1/6.0 cm = (-1 - 8)/8u

-1/6.0 cm = -9/8u

Cross-multiplying:

-1 * 8u = -9 * 6.0 cm

-8u = -54 cm

Dividing by -8:

u = -6.75 cm

Therefore, the object should be placed at a distance of 6.75 cm from the mirror to obtain an image that is 48 cm tall.

To find the distance at which the object should be placed from the mirror to obtain the desired image height, we can use the mirror formula:

1/f = 1/v - 1/u

Where:
- f is the focal length of the mirror
- v is the distance of the image from the mirror
- u is the distance of the object from the mirror

We know the focal length of the mirror can be calculated using the formula:

f = R/2

Where R is the radius of curvature of the mirror.

Given that the radius of curvature of the mirror is 6.0 cm, the focal length can be calculated as follows:

f = 6.0 cm / 2 = 3.0 cm

Now we can substitute the values into the mirror formula:

1/3.0 cm = 1/48 cm - 1/u

Simplifying the equation:

1/3.0 cm = (1 - 48/u) / 48 cm

Cross-multiplying:

48 cm / 3.0 cm = 1 - 48/u

16 = 1 - 48/u

Rearranging the equation to solve for u:

48/u = 1 - 16

48/u = -15

u = 48 cm / -15

u ≈ -3.2 cm

Since the distance cannot be negative, we discard the negative sign and the object should be placed approximately 3.2 cm away from the concave mirror to obtain an image that is 48 cm tall.