A small cup of green tea is positioned on the central axis of a spherical mirror. The lateral magnification of the cup is +0.312, and the distance between the mirror and its focal point is 2.48 cm. What is the distance between the mirror and the image it produces?
To find the distance between the mirror and the image it produces, we can use the mirror formula:
1/f = 1/u + 1/v
Where:
f = focal length of the mirror
u = distance of the object from the mirror (negative if the object is on the same side as the incident light)
v = distance of the image from the mirror (negative if the image is on the same side as the incident light)
In this case, the mirror is a concave mirror because we have a positive lateral magnification. The focal length (f) is given as 2.48 cm, and the lateral magnification (m) is +0.312. We need to find the distance between the mirror and the image (v).
First, we need to find the distance of the object (u) from the mirror. Since the cup is positioned on the central axis, the distance of the object from the mirror is equal to the focal length (f). Therefore, u = f = 2.48 cm.
Using the formula for lateral magnification:
m = -v/u
Plugging in the values we know:
0.312 = -v/(2.48)
Rearranging the equation to solve for v:
v = -0.312 * 2.48
v = -0.77216 cm
Since the distance of the image (v) is negative, it means the image is formed on the same side as the incident light. Thus, the distance between the mirror and the image it produces is approximately 0.77216 cm.