Answer :
A concave mirror, also known as a converging mirror or a concave spherical mirror, is a mirror with a curved reflective surface that bulges inward. The object must be placed at a distance of 38.6 cm from the concave mirror.
To determine the distance at which an object must be placed from a concave mirror in order for its image to be at infinity, 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 (positive for real images, negative for virtual images)
u is the object distance (positive for objects on the same side as the incident light, negative for objects on the opposite side)
In this case, since the image is at infinity, the image distance (v) is infinite. Therefore, we can simplify the mirror formula as follows:
1/f = 0 - 1/u
Simplifying further, we have:
1/f = -1/u
Since the mirror is concave, the focal length (f) is negative. Therefore, we can rewrite the equation as:
-1/f = -1/u
By comparing this equation with the general form of a linear equation (y = mx), we can see that the slope (m) is -1 and the intercept (y-intercept) is -1/f.
Therefore, the object distance (u) should be equal to the focal length (f) for the image to be at infinity.
Given that the radius of the concave mirror is 38.6 cm, the focal length (f) is half of the radius:
f = 38.6 cm / 2 = 19.3 cm
Therefore, the object must be placed at a distance of 19.3 cm (or approximately 38.6 cm) from the concave mirror for its image to be at infinity.
To achieve an image at infinity with a concave mirror (radius 38.6 cm), the object must be placed at a distance of approximately 38.6 cm from the mirror.
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Final answer:
To place an object so its image is at infinity in a concave mirror, it must be placed at the focal point. For a concave mirror with a given radius of curvature of 38.6 cm, the focal length will be half of this, so the object should be placed 19.3 cm away from the mirror.
Explanation:
The subject of your question falls under Physics, specifically the topic of optics dealing with concave mirrors. In order to determine how far an object must be placed from a concave mirror so that its image is at infinity, we need to understand the mirror equation and the principle of a focal point.
A concave mirror has a focal point, which is the point at which all light rays parallel to the axis of the mirror converge. If an object is placed at the focal point of a concave mirror, the light rays reflecting off the mirror will be parallel and the image will appear at infinity.
Since the radius of curvature of the mirror (R) is given as 38.6 cm, the focal length (f) of the mirror would be half of this value, which is 19.3 cm. As a result, to get an image at infinity, the object must be placed 19.3 cm away from the concave mirror. This is because if an object is placed at the focal point of a concave mirror, the reflected rays are parallel and seem to come from a point at infinity.
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