A candle, 3.5 cm high, placed 29 cm in front of a curved mirror forms an image at a distance of 12 cm from the mirror.
Focal length of mirror?
How high is the image?
What type of mirror is this?
To find the focal length of the mirror, we can use the mirror formula, which states:
1/f = 1/v - 1/u,
where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror.
In this case, the distance of the image (v) is given as 12 cm, and the distance of the object (u) is given as 29 cm. We can plug these values into the formula and solve for f:
1/f = 1/12 - 1/29.
To simplify the equation, we can find a common denominator:
1/f = (29 - 12) / (12 * 29).
1/f = 17 / (12 * 29).
Now, we can invert both sides of the equation to solve for f:
f = (12 * 29) / 17.
Evaluating this expression, we find that the focal length of the mirror is approximately 20.47 cm.
To find the height of the image, we can use the magnification formula, which states:
h'/h = -v/u,
where h' is the height of the image and h is the height of the object.
In this case, the height of the object (h) is given as 3.5 cm, and the distance of the image (v) is given as 12 cm. We can plug these values into the formula and solve for h':
h'/3.5 = -12/29.
To solve for h', we can cross multiply:
h' = (3.5 * -12) / 29.
Evaluating this expression, we find that the height of the image is approximately -1.43 cm. The negative sign indicates that the image is inverted.
To determine the type of mirror, we can use the magnification formula. Since the height of the image (h') is negative, it implies that the image is inverted. In the case of curved mirrors, an inverted image is formed by a concave mirror. Therefore, the type of mirror in this scenario is a concave mirror.