fical lengt of concave mirror =50cm m=1÷2 cm .find the position of the object
To find the position of the object in front of a concave mirror, you can use the mirror formula, which is:
1/f = 1/v - 1/u
Where:
- f is the focal length of the concave mirror.
- v is the image distance (distance between the mirror and the image).
- u is the object distance (distance between the mirror and the object).
In this case, the focal length (f) of the concave mirror is given as 50 cm.
The magnification (m) is given as 1/2 cm.
The magnification (m) is defined as the ratio of the height of the image to the height of the object. It can also be written as:
m = -v/u
Since m is given as 1/2 cm, we can substitute it into the magnification equation:
1/2 cm = -v/u
Now we have two equations:
1/f = 1/v - 1/u
1/2 cm = -v/u
To solve these equations, we need to identify two unknowns (v and u). However, we have two equations, so we can solve them simultaneously.
By substitution, we can solve for v:
1/2 cm = -v/u
Cross-multiplying, we get:
2u = -v
Now substitute this value of v in the mirror formula equation:
1/f = 1/v - 1/u
1/50 cm = 1/(-2u) - 1/u
Simplifying, we get:
1/50 cm = (-1 - 2)/(-2u)
1/50 cm = -3/(-2u)
Cross-multiplying, we get:
-2u = -150 cm
Dividing by -2, we get:
u = 75 cm
Therefore, the position of the object in front of the concave mirror is 75 cm from the mirror.