describe fully the image of a candle flame located 10 cm from a concave spherical mirror with a radius of curvature of 16 cm
To describe the image of a candle flame located 10 cm from a concave spherical mirror with a radius of curvature of 16 cm, we can use the mirror equation and magnification equation.
1. Mirror Equation:
The mirror equation gives us the relationship between the object distance (o), the image distance (i), and the focal length (f) of the mirror. It is given by:
1/f = 1/o + 1/i
In this case, since the mirror is concave, the focal length (f) is negative (-16 cm). The object distance (o) would be 10 cm since the candle is located 10 cm in front of the mirror. We can solve for the image distance (i) using the mirror equation.
1/(-16) = 1/10 + 1/i
-1/16 = 1/10 + 1/i
-6/80 = 1/i
i = -80/6 = -13.33 cm (Approximately)
So, the image distance (i) is approximately -13.33 cm. The negative sign indicates that the image is formed on the same side as the object (real image).
2. Magnification:
The magnification equation gives us the relationship between the height of the image (hi) and the height of the object (ho). It is given by:
magnification (m) = hi / ho = -i / o
In this case, since the image distance (i) is negative (-13.33 cm) and the object distance (o) is positive (10 cm), the magnification would also be negative. We can solve for the magnification (m) using the given values.
m = -13.33 / 10 = -1.333 (Approximately)
So, the magnification (m) is approximately -1.333. The negative sign indicates that the image is inverted compared to the object.
In conclusion, the image of the candle flame located 10 cm from the concave spherical mirror with a radius of curvature of 16 cm is a real and inverted image with an image distance of approximately -13.33 cm and a magnification of approximately -1.333.