The focal length of a concave mirror, that produces four times larger real image of an object placed at 5 cm distance from the mirror, is------
u=-5cm
f= ?
m=-4
magnification will be negative as the image is real.
m=-v/u
-4=-v/-5
v=-20
1/f= 1/v+ 1/u
1/f= -1/20-1/5
1/f= -1-4/20
1/f=-5/20
f= 4
The focal length of the concave mirror is 4 cm.
To find the focal length of 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 between the image and the mirror)
- u is the object distance (distance between the object and the mirror)
In this case, we are given that the concave mirror produces a four times larger real image of an object placed at a 5 cm distance from the mirror. So, we have:
v = 4u
Substituting this value of v into the mirror formula, we get:
1/f = 1/(4u) - 1/u
Simplifying further:
1/f = (1 - 4)/4u
1/f = -3/4u
Now, we can substitute the object distance u = 5 cm:
1/f = -3/(4 * 5)
1/f = -3/20
To find the focal length, we can take the reciprocal of both sides:
f = -20/3
Therefore, the focal length of the concave mirror is -20/3 cm. Note that the negative sign indicates that the mirror is concave.