Step-by-step explanation:
To calculate the radius of curvature of a concave makeup mirror that produces an upright image at a distance of 50 cm behind the mirror when an object is placed 25 cm in front of it, you can use the formula:
R = 2f
where R is the radius of curvature and f is the focal length of the mirror.
To find the focal length of the mirror, you can use the formula:
1/di + 1/do = 1/f
where di is the distance of the image from the mirror, do is the distance of the object from the mirror, and f is the focal length of the mirror.
In this case, do is equal to 25 cm, and di is equal to 50 cm. Plugging these values into the formula gives:
1/50 cm + 1/25 cm = 1/f
Solving for f gives:
f = (50 cm * 25 cm) / (25 cm - 50 cm) = -25 cm
Since the focal length is negative, this indicates that the mirror is concave.
Plugging the value for f into the formula for the radius of curvature gives:
R = 2 * (-25 cm) = -50 cm
This means that the radius of curvature of the mirror is 50 cm.
To calculate the magnification of the image, you can use the formula:
m = -di/do
Plugging in the values for di and do gives:
m = (-50 cm)/(25 cm) = -2
This means that the magnification of the image is -2.
Since the magnification is negative, the image is virtual and is located on the same side of the mirror as the object. Additionally, since the magnification is less than 1, the image is inverted relative to the object.