The image of a candle flame placed at a distance of 30 cm from a mirro...
Nature of the mirror
The image of the candle flame is formed on the other side of the mirror, which means that the mirror is a concave mirror. This is because the image formed is real, inverted, and smaller in size than the object.
Focal length of the mirror
The formula to calculate the focal length of a concave mirror is:
1/f = 1/v + 1/u
Where:
- f = focal length of the mirror
- v = distance of the image from the mirror
- u = distance of the object from the mirror
Here, the distance of the object from the mirror is given as 30 cm (since the candle flame is placed at a distance of 30 cm from the mirror). The distance of the image from the mirror can be calculated using the formula:
1/f = 1/v - 1/u
Substituting the values, we get:
1/f = 1/60 - 1/30
Solving for f, we get:
f = -60 cm
Since the focal length has a negative value, it means that the mirror is a concave mirror.
Height of the image
The magnification formula for a concave mirror is:
m = -v/u
Where:
- m = magnification
- v = distance of the image from the mirror
- u = distance of the object from the mirror
Substituting the values, we get:
m = -60/30 = -2
Since the magnification is negative, it means that the image is inverted. The height of the image can be calculated using the formula:
hi = m x ho
Where:
- hi = height of the image
- m = magnification
- ho = height of the object
Substituting the values, we get:
hi = -2 x 2.4 cm = -4.8 cm
Since the height of the image has a negative value, it means that the image is also inverted.