An object located 15cm in front of a concave mirror of radius 0.5cm. the magnification of the image is
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An object located 15 cm in front of a concave mirror of radius 0.5 cm. tthe magnification of the image is
To determine the magnification of an image formed by a concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the mirror
- v is the image distance (distance of the image from the mirror)
- u is the object distance (distance of the object from the mirror)
First, we need to find the focal length (f) of the concave mirror. The focal length of a concave mirror is half the radius of curvature (R):
f = R/2
Given that the radius (R) of the mirror is 0.5 cm, we can calculate the focal length:
f = 0.5 cm / 2 = 0.25 cm
Next, we need to calculate the image distance (v). Since the mirror is concave and the object is located in front of it, the image will be formed on the same side as the object. In this case, the image distance (v) will be positive.
Given that the object distance (u) is 15 cm, we can rearrange the mirror formula to solve for v:
1/v = 1/f + 1/u
Substituting the values, we get:
1/v = 1/0.25 + 1/15
Now, solve for 1/v:
1/v = (1/0.25) + (1/15)
1/v = 4 + 0.0667
1/v = 4.0667
Finally, solve for v:
v = 1/1/v
v = 1/4.0667
v ≈ 0.2457 cm
The image distance (v) is approximately 0.2457 cm.
To calculate the magnification (m), we can use the formula:
m = -v/u
Substituting the values:
m = -(0.2457 cm) / (15 cm)
m ≈ -0.0164
The magnification of the image formed by the concave mirror is approximately -0.0164. Note that the negative sign indicates that the image is inverted.