what is the focal lenght of an object 10cm in front of a convex mirror having image that is 5cm behind the mirror?
To find the focal length of a convex mirror, you can make use of the mirror formula:
1/f = 1/v + 1/u
where:
- f is the focal length
- v is the image distance (distance of the image from the mirror)
- u is the object distance (distance of the object from the mirror)
Given:
- u = -10 cm (negative sign indicates that the object is in front of the mirror)
- v = -5 cm (negative sign indicates that the image is behind the mirror)
Plugging these values into the formula:
1/f = 1/v + 1/u
1/f = 1/(-5 cm) + 1/(-10 cm)
Now, calculate the values:
1/f = -1/5 cm + -1/10 cm
Simplifying the equation:
1/f = (-2 - 1) / 10 cm
1/f = -3 / 10 cm
To isolate f, invert both sides of the equation:
f = 10 cm / -3
Simplifying further:
f ≈ -3.33 cm
Therefore, the focal length of the convex mirror is approximately -3.33 cm.
To find the focal length of a convex mirror, you 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 of the image from the mirror)
- u is the object distance (distance of the object from the mirror)
In this case, the object distance (u) is given as -10 cm (since it is 10 cm in front of the mirror) and the image distance (v) is given as 5 cm (since the image is 5 cm behind the mirror).
Substituting these values into the mirror formula:
1/f = 1/5 - 1/-10
To simplify, we need to find the least common multiple (LCM) of the denominators:
1/f = 2/10 - 1/10
1/f = 1/10
Therefore, the focal length (f) of the convex mirror is 10 cm.