An object is placed at a distance of 6 cm from a concave mirror and an image is produced at a distance at a distance of 14 cm from the mirror. What is the focal length?
To find the focal length of a concave mirror, you can use the mirror formula which is given by:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance
u = object distance
In this case, the object distance (u) is given as 6 cm and the image distance (v) is given as 14 cm.
Let's substitute the values into the formula:
1/f = 1/14 - 1/6
To solve this equation, we need to find a common denominator for the fractions. The common denominator here is 42:
1/f = (3/42) - (7/42)
Combining the fractions:
1/f = -4/42
Now, invert both sides to get the value of f:
f = -42/4
f = -10.5 cm
Therefore, the focal length of the concave mirror is -10.5 cm. The negative sign indicates that the mirror is concave.