Table of Contents
What is the relation between radius of curvature and aperture?
The relation between focal length (f) and radius of curvature (R) of a spherical mirror is that the focal length is equal to half of the radius of curvature i.e. f=R2. Let us derive this relation. Consider a concave mirror such that its radius of curvature is very much larger than the diameter of its aperture.
What is the relation between focal length and radius of curvature of a spherical mirror Class 10?
For a spherical mirror the principal focus (F) lies exactly mid-way between the pole (P) and centre of curvature (C). So, the focal length (f) of a spherical mirror is equal to half of its radius of curvature (R).
What is relation between F and R?
Focal length and radius of curvature are related as: f=2R.
Is aperture and radius of curvature same?
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. Aperture is the entire area of the reflecting surface of the spherical mirror.
Why is R 2f?
R is the radius of curvature and f is the focal length of a spherical mirror. For spherical mirrors of small apertures, the radius of curvature is found to be equal to twice the focal length, i.e., R = 2f. This implies that the principal focus of a spherical mirror lies between the pole and the centre of curvature.
What happens when aperture is more than radius of curvature?
For a spherical mirror the diameter of the aperture cannot be over twice the radius of curvature. Such a mirror would have an enormous aberration. Such a mirror would have a serious aberration not all the incident light would focus within an equivalent spot unless it emanates from the center of curvature.
What is the relation between focal length and radius of curvature of a plano convex lens?
The focal length of a plano-convex lens is equal to its radius of curvature.
What is the relation between F and 2f?
The relationship between the focal length f and radius of curvature r is r = 2f.
Can aperture be smaller than radius of curvature?
For a truly spherical mirror, the diameter of the aperture cannot be more than twice the radius of curvature (that’s just how big a sphere is if you cut it exactly in half).
Is C and 2F same?
Answer: Yes the centre of curvature C and 2F are same. The centre of the curvature of the spherical lens is at the double of the focal length from the pole of the mirror located on the principal axis.
What is U and V in ray optics?
The image distance ( v ) is plotted against the object distance ( u ) for a concave mirror of focal length f .
Why aperture should be less than radius of curvature?
So, using an aperture much smaller than the radius of the mirror is to restrict the incoming light to a region where rays do come to a single focal point.