The focal length of a small concave mirror is 2.5cm in order to use this mirror by dentist .The distance of tooth from mirror is
Less than 2.5cm
Physics problems
The distance of the tooth from the concave mirror can be determined using the mirror equation:
1/f = 1/v - 1/u
Where:
f is the focal length of the mirror (2.5 cm in this case)
v is the image distance from the mirror
u is the object distance from the mirror (distance of the tooth from the mirror)
Since the mirror is concave and the image formed is virtual, the image distance (v) is negative.
Assuming the dentist wants to use the mirror to see a magnified virtual image of the tooth, we can use v = -2f.
Plugging in the values, we have:
1/2.5 = 1/(-2f) - 1/u
Simplifying, we get:
0.4 = -0.5/f - 1/u
Now, substituting f = 2.5 cm:
0.4 = -0.5/2.5 - 1/u
Simplifying further:
0.4 = -0.2 - 1/u
Rearranging the equation:
0.4 + 0.2 = -1/u
0.6 = -1/u
To solve for u, we need to take the reciprocal of both sides:
1/u = -0.6
u = -1/0.6
u = -1.67 cm
Therefore, the distance of the tooth from the mirror is approximately -1.67 cm.
To find the distance of the tooth from the small 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 of the tooth from the mirror)
- u is the object distance (distance of the tooth from the mirror)
Given that the focal length (f) is 2.5 cm, we can substitute it into the formula:
1/2.5 = 1/v - 1/u
Since the mirror is a concave mirror and used in a dentist's setting, we assume that the object (the tooth) is real and placed in front of the mirror, so the object distance (u) is positive.
Now, let's assume that the final image is formed at a distance (v) very close to the focal length (f). In this case, we can approximate that the image distance (v) is approximately equal to the focal length (f).
Substituting v = f in the formula gives:
1/2.5 = 1/f - 1/u
Since v = f, the equation becomes:
1/2.5 = 1/2.5 - 1/u
Simplifying this equation:
1/2.5 - 1/2.5 = -1/u
0 = -1/u
Since 0 is equal to -1/u, it means that u is equal to infinity. This implies that the distance of the tooth from the mirror is infinity, which is not physically plausible.
Hence, based on the given information and assumptions, it is not possible to determine the exact distance of the tooth from the small concave mirror.