The focal length of a concave mirror that produces four times larger real image of an object held at 5cm from the mirror is.....
To determine the focal length of a concave mirror, we can use the mirror formula:
1/f = 1/v - 1/u
where:
- f represents the focal length of the mirror
- v represents the image distance (distance of the image from the mirror)
- u represents the object distance (distance of the object from the mirror)
We are given that the concave mirror produces a four times larger real image of an object. Let's assume the magnification factor as M.
M = -v/u
Since the magnification factor M is 4, we can rewrite the equation as:
4 = -v/u
We know that the object distance (u) is 5 cm. Therefore, substituting this value into the equation, we have:
4 = -v/5
To solve for v, we can rearrange the equation:
v = -4 * 5
v = -20 cm
Now that we have the image distance (v), we can substitute this value into the mirror formula to find the focal length (f):
1/f = 1/v - 1/u
1/f = 1/(-20) - 1/5
Simplifying further:
1/f = -1/20 - 1/5
1/f = (-1 - 4)/20
1/f = -5/20
1/f = -1/4
To obtain the focal length (f), we take the reciprocal of both sides of the equation:
f = -4/1
f = -4 cm
The focal length of the concave mirror that produces a four times larger real image of an object held at 5 cm from the mirror is -4 cm. Note that the negative sign indicates that the mirror is concave.
To find the focal length of a concave mirror that produces a four times larger real image of an object, we can use the mirror formula:
1/f = 1/v - 1/u
Where:
f = focal length of the mirror
v = image distance from the mirror
u = object distance from the mirror
Given:
v = -4u (image is four times larger than the object)
u = 5cm
Substituting these values into the mirror formula, we get:
1/f = 1/(-4u) - 1/u
Simplifying, we have:
1/f = -1/4u - 1/u
Combining the fractions, we get:
1/f = -5/(4u)
Substituting the value of u into the equation, we have:
1/f = -5/(4 * 5)
Simplifying further:
1/f = -5/20
Dividing both sides by -5:
1/f = -1/4
To find the focal length, we take the reciprocal of both sides:
f = -4cm
Therefore, the focal length of the concave mirror is -4cm. Note that the negative sign indicates a concave mirror.