Explain the meaning of these terms with reference to a concave mirror: radius of curvature, principal focus, and aperture.
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Ah, terminology questions. Fun.
Let's take them one at a time.
- Radius of Curvature -- This has to do with how "curved" the mirror is. Is it almost flat, or does it form an elongated "U" shape? This will have a lot to do with the focusing power of the concave mirror.
- Principal Focus -- This is the point on the mirror that the reflected light is aiming toward (in a concave mirror) or aiming away from (in a convex mirror.)
- Aperture -- This is how much light the mirror is able to focus. It is a measure of how much light can hit the mirror. It is both a product of how big the mirror itself is, and how much light is allowed to hit it (as if the mirror had a black piece of paper over it with a tiny hole, for example.)
Hope these examples help clear up any questions you had about these terms!
Radius of curvature:
Radius curvature of a spherical mirror (both concave and convex) is the radius of the sphere of which the the mirror is a part.
The principal focus of a spherical concave mirror is defined as a point on its principal axis where a beam of light parallel to the principal axis converges after being reflected by the mirror. In case of convex mirror the light only appears to converge at principal focus after being reflected by the mirror.
Aperture of a spherical mirror refers to the effective size of the mirror that is used in a device. For a round spherical mirror (both concave and convex) the linear aperture is defined as the distance between extreme points in the periphery of a mirror.
The concave mirror is a spherical mirror whose reflection surface is a section of an inner surface of a hollow sphere.
The Centre of curvature of the concave mirror is the centre of the sphere of which the concave mirror is a part.
The centre of the reflecting surface of the concave mirror is the pole of the concave mirror.
Radius of curvature of is the radius of the sphere whose section is the reflection surface of the concave mirror.
The line through the centre of curvature and the pole of the concave mirror is called the principal axis.
The Principal focus is a point on the principal axis through which if a ray is incident on the mirror, then it gets reflected parallel to principal axis. All rays that are incident parallel to principal axis gets reflected through principal axis. It lies approximately half way between the centre of curvature and the pole of the mirror.
Aperture is the entire area of the reflecting surface of the spherical mirror.
The concave mirror is a spherical mirror whose reflecting surface forms a section of the interior of a hollow sphere.
Radius of curvature of a concave mirror is the radius of the sphere of whose section is the reflecting surface of the concave mirror.
The Principal focus is the point on the principal axis through which if a ray is incident on the mirror, then it gets reflected parallel to principal axis. All rays that are incident parallel to principal axis converge and get reflected through the principal axis. Since all the rays converge at the principal focus this point is very hot and can be used to start a fire.
Aperture is the entire area of the reflecting surface of the spherical mirror. It is measured as the distance between the extreme points in the edges of the mirror.
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