To calculate the position, nature, and magnification of the image produced by a concave mirror, we can use the mirror equation and magnification formula.
Given:
Object distance (u) = -10 cm (negative sign indicates the object is in front of the mirror)
Radius of curvature (R) = -10 cm (negative sign indicates a concave mirror)
Using the mirror equation:
1/f = 1/v - 1/u
Since the radius of curvature (R) is twice the focal length (f) for a concave mirror, we can substitute R = -2f into the equation:
1/(-2f) = 1/v - 1/u
Simplifying the equation:
-1/2f = 1/v - 1/u
Now, substitute the given values:
-1/2f = 1/v - 1/(-10 cm)
To solve for v, we need to solve the equation above.
To determine the nature of the image, we consider the following scenarios:
- If v is positive, the image is formed on the same side as the object (real image).
- If v is negative, the image is formed on the opposite side as the object (virtual image).
To find the magnification (m), we can use the formula:
m = -v/u
Now, let's calculate the position, nature, and magnification of the image.
Substituting the values into the equation and solving for v:
-1/2f = 1/v + 1/10 cm
Simplifying the equation:
-1/2f - 1/10 cm = 1/v
Combining the fractions:
(-5 cm - f) / (10f cm) = 1/v
Multiplying both sides by v:
v(-5 cm - f) / (10f cm) = 1
Simplifying:
v = (10f cm) / (-5 cm - f)
Substituting the value of f (focal length) for a concave mirror (R/2 = -10 cm/2 = -5 cm):
v = (10(-5 cm) cm) / (-5 cm - (-5 cm))
v = 50 cm / 0
v = Undefined (Division by zero)
Based on the calculation, we can observe that the image position is undefined. This indicates that no image is formed by the concave mirror in this scenario.