What should the radius of curvature of the mirror be

B 24cm. What is the man''s Density of the liquid. Acceleration due to gravity. Type of container Which of the following ammeters may be used to measure alternating currents? If the total force acting on a particle is zero, the linear momentum will The process whereby a liquid turns spontaneously into vapour is called? Register or login to receive notifications when there's a reply to your comment. Don't want to keep filling in name and email whenever you want to comment?

Register or login to make commenting easier. Save my name, email, and website in this browser for the next time I comment. Toggle navigation. Search Log In. A concave mirror has a radius of curvature of 36cm. Question A concave mirror has a radius of curvature of 36cm.

At what distance from the mirror should an object be placed to give a real image three times the size of the object? Options A 12cm B 24cm C 48cm D cm. The distance along the optical axis from the mirror to the focal point is called the focal length of the mirror. Thus, the focal point is virtual because no real rays actually pass through it; they only appear to originate from it. The incident ray is parallel to the optical axis.

The point at which the reflected ray crosses the optical axis is the focal point. Note that all incident rays that are parallel to the optical axis are reflected through the focal point—we only show one ray for simplicity. In this chapter, we assume that the small-angle approximation also called the paraxial approximation is always valid. In this approximation, all rays are paraxial rays, which means that they make a small angle with the optical axis and are at a distance much less than the radius of curvature from the optical axis.

To find the location of an image formed by a spherical mirror, we first use ray tracing, which is the technique of drawing rays and using the law of reflection to determine the reflected rays later, for lenses, we use the law of refraction to determine refracted rays.

Combined with some basic geometry, we can use ray tracing to find the focal point, the image location, and other information about how a mirror manipulates light.

In fact, we already used ray tracing above to locate the focal point of spherical mirrors, or the image distance of flat mirrors. To locate the image of an object, you must locate at least two points of the image. Locating each point requires drawing at least two rays from a point on the object and constructing their reflected rays.

The point at which the reflected rays intersect, either in real space or in virtual space, is where the corresponding point of the image is located. These are the objects whose images we want to locate by ray tracing. We choose to draw our ray from the tip of the object.

The reflection of this ray must pass through the focal point, as discussed above. For the convex mirror, the backward extension of the reflection of principal ray 1 goes through the focal point i. Principal ray 2 travels first on the line going through the focal point and then is reflected back along a line parallel to the optical axis. Principal ray 3 travels toward the center of curvature of the mirror, so it strikes the mirror at normal incidence and is reflected back along the line from which it came.

Finally, principal ray 4 strikes the vertex of the mirror and is reflected symmetrically about the optical axis. We are thus free to choose whichever of the principal rays we desire to locate the image. Drawing more than two principal rays is sometimes useful to verify that the ray tracing is correct. To completely locate the extended image, we need to locate a second point in the image, so that we know how the image is oriented. To do this, we trace the principal rays from the base of the object.

In this case, all four principal rays run along the optical axis, reflect from the mirror, and then run back along the optical axis.

The difficulty is that, because these rays are collinear, we cannot determine a unique point where they intersect. All we know is that the base of the image is on the optical axis. However, because the mirror is symmetrical from top to bottom, it does not change the vertical orientation of the object.

Thus, because the object is vertical, the image must be vertical. Therefore, the image of the base of the object is on the optical axis directly above the image of the tip, as drawn in the figure.

For the concave mirror, the extended image in this case forms between the focal point and the center of curvature of the mirror. It is inverted with respect to the object, is a real image, and is smaller than the object. Were we to move the object closer to or farther from the mirror, the characteristics of the image would change.

For example, we show, as a later exercise, that an object placed between a concave mirror and its focal point leads to a virtual image that is upright and larger than the object. For the convex mirror, the extended image forms between the focal point and the mirror.

It is upright with respect to the object, is a virtual image, and is smaller than the object. Ray tracing is very useful for mirrors. The rules for ray tracing are summarized here for reference:. We use ray tracing to illustrate how images are formed by mirrors and to obtain numerical information about optical properties of the mirror. If we assume that a mirror is small compared with its radius of curvature, we can also use algebra and geometry to derive a mirror equation, which we do in the next section.

Combining ray tracing with the mirror equation is a good way to analyze mirror systems. For a plane mirror, we showed that the image formed has the same height and orientation as the object, and it is located at the same distance behind the mirror as the object is in front of the mirror.

Although the situation is a bit more complicated for curved mirrors, using geometry leads to simple formulas relating the object and image distances to the focal lengths of concave and convex mirrors. The law of reflection tells us that they have the same magnitude, but their signs must differ if we measure angles from the optical axis.

No approximation is required for this result, so it is exact. Although it was derived for a concave mirror, it also holds for convex mirrors proving this is left as an exercise. We can extend the mirror equation to the case of a plane mirror by noting that a plane mirror has an infinite radius of curvature. This means the focal point is at infinity, so the mirror equation simplifies to.

Notice that we have been very careful with the signs in deriving the mirror equation. For a plane mirror, the image distance has the opposite sign of the object distance. In this case, the image height should have the opposite sign of the object height.

To keep track of the signs of the various quantities in the mirror equation, we now introduce a sign convention. Using a consistent sign convention is very important in geometric optics. It assigns positive or negative values for the quantities that characterize an optical system.

Understanding the sign convention allows you to describe an image without constructing a ray diagram. This text uses the following sign convention:. Notice that rule 1 means that the radius of curvature of a spherical mirror can be positive or negative.

What does it mean to have a negative radius of curvature? This means simply that the radius of curvature for a convex mirror is defined to be negative. In deriving this equation, we found that the object and image heights are related by.

The highest point of the object is above the optical axis, so the object height is positive. The image, however, is below the optical axis, so the image height is negative. Thus, this sign convention is consistent with our derivation of the mirror equation. With this definition of magnification, we get the following relation between the vertical and horizontal object and image distances:. This is a very useful relation because it lets you obtain the magnification of the image from the object and image distances, which you can obtain from the mirror equation.

One of the solar technologies used today for generating electricity involves a device called a parabolic trough or concentrating collector that concentrates sunlight onto a blackened pipe that contains a fluid. This heated fluid is pumped to a heat exchanger, where the thermal energy is transferred to another system that is used to generate steam and eventually generates electricity through a conventional steam cycle.

The real mirror is a parabolic cylinder with its focus located at the pipe; however, we can approximate the mirror as exactly one-quarter of a circular cylinder. First identify the physical principles involved. Part a is related to the optics of spherical mirrors. Part b involves a little math, primarily geometry. Part c requires an understanding of heat and density. The area for a length of 1. We are considering only one meter of pipe here and ignoring heat losses along the pipe.

A keratometer is a device used to measure the curvature of the cornea of the eye, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the magnification of the image.