AN OBJECT OF HEIGHT 5CM IS PLACED INFRONT OF ACONCAVE MIRROR OF FOCAL LENGTH 6CM AT ADISTANCE 13CM .FIND IMAGE POSITION MAGNIFICATION IMAGE PROPERTIES
To find the image position, magnification, and image properties of an object placed in front of a concave mirror, we can use the mirror formula and magnification formula.
1. Mirror Formula:
The mirror formula is given as:
1/f = 1/v - 1/u
Where:
- f is the focal length of the concave mirror
- v is the image distance from the mirror (positive if the image is real and negative if the image is virtual)
- u is the object distance from the mirror (positive if the object is in front of the mirror and negative if the object is behind the mirror)
2. Magnification Formula:
The magnification formula is given as:
magnification (m) = -v/u
From the given information, we know:
- Object height (h) = 5 cm
- Focal length (f) = 6 cm
- Object distance (u) = -13 cm (negative because the object is placed in front of the mirror)
Now, let's calculate:
1. Image Position (v):
Using the mirror formula, we can calculate the image position.
1/f = 1/v - 1/u
1/6 = 1/v - 1/(-13)
1/6 = 1/v + 1/13 (taking the negative sign to the right side)
Multiply both sides by 6v:
v = 13 + 6*13/6
v = 13 + 13
v = 26 cm
The image position is 26 cm (positive, indicating a real image since it is on the same side as the object).
2. Magnification (m):
Using the magnification formula, we can calculate the magnification.
magnification (m) = -v/u
m = -26/-13
m = 2
The magnification is 2.
3. Image Properties:
Based on the magnification value, we can determine the image properties.
- If |m| > 1, the image is magnified.
- If |m| = 1, the image is the same size as the object (neither magnified nor diminished).
- If 0 < |m| < 1, the image is diminished.
Since the magnification value is 2 (greater than 1), the image formed by the concave mirror is magnified.
Therefore, the image position is 26 cm (real image), the magnification is 2 (magnified), and the image properties are magnified.