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Spherical Mirror Formula

Last updated date: 20th Feb 2024
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What are Spherical Mirrors?

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The mirrors which we use in the cars to see the back side are known as the spherical mirrors. The mirrors which are the spherical one, are the mirrors having curved surfaces that are painted on one of their sides. The spherical mirror is a mirror in which inward surfaces are painted and are called convex mirrors while the mirrors in which outward surfaces are painted are called concave mirrors. In this article we are going to discover more about the topic.

Surface Area of a Cylinder

A cylinder generally is a three-dimensional structure having circular bases parallel to each other. Generally we see that the area of the three-dimensional shapes refers to the surface area. The surface area that is represented is in the units of square. For example we can say that cm2, m2, and so on etc. A cylinder which we are talking here can be seen as a set of circular disks that are stacked on one another.  Since we see that the cylinder is a solid of a shape which is three-dimensional  it has both volume and surface area. 

The area of the cylinder is defined as the sum of the curved surface and the area of two circular bases of the cylinder.

The area of the cylinder is said to be the total region which is covered by a cylinder in three-dimensional space. The area of a cylinder is said to be equal to the sum of the area of two circular bases and curved in area of surface. In right cylinders the two bases which are circular are exactly over each other and the axis line produces a right angle to the base. In case if one of the bases which is circular  is displaced and the axis does not produce the right angle to the base then it is known as the oblique cylinder.

In the middle of the two bases of  circular, there is a surface which is curved which when opened generally represents a rectangular shape. This is a curved surface and is also known as the lateral surface. The different parameters that are used to calculate the area of the cylinder include height and radius, axis, base, and side. The radius which is of the cylinder is generally defined as the radius of the circular base.

Surface Area of a Sphere

 A Sphere that is a three-dimensional solid is having a round shape that is just like a circle. The formula which is of total surface area of a sphere that too in terms of pi denoted by π is given by:

The surface area is given as =  4 π r2 square units

The difference between a sphere and a circle is that a circle is a figure which is two-dimensional or we can say that a flat shape whereas a sphere is a shape which is three-dimensional. Therefore we can say that the area of the circle is different from the area of the sphere. 

Area of circle is denoted as = π r2 

From a perspective which is visual, a sphere has a three-dimensional structure that forms by rotating a disc that is circular with one of the diagonals.

Let us consider that an instance where spherical ball faces are painted. To paint the whole surface we can see that the paint quantity required has to be known beforehand. Hence the area which is of every face has to be known to calculate the quantity of the paint for painting the same. We can generally define this term as the total surface area.

The surface area that is of a sphere is equal to the area of the entire face surrounding it.

Surface Area of a Cone

The Cone is said to be a structure which is three-dimensional which has a circular base where a set of line segments connect all of the points on the base to a common point called apex. A cone can be seen as a set of circular non-congruent discs that are stacked on one another in such a manner that the ratio of the radius of adjacent discs remains constant. We can think of a cone as a triangle which is being rotated about one of its own vertices. That is the curved surface area of a cone = πrl

And the total surface area of a cone = πr(l+r)

The curved surface which is of a cone is the area of the cone that is excluding the base. In other words we can say that it is the area of the cone when it is unfolded. The formula which is to calculate the curved surface area that too of a cone is given by:

The curved Surface Area that is the CSA = πrl

Here we can see that:

Letter r = is the radius of the circular base of the cone

Letter l = is the slant height of the cone

FAQs on Spherical Mirror Formula

1. Explain what are the characteristics of spherical mirrors?

The spherical Mirrors

  • There are two kinds of spherical mirrors that are the convex and the  concave.

  • The focal point that is denoted by letter F of a concave mirror is the point at which a parallel beam of light is "focussed" after reflection in the mirror. 

  • We can say that the focal length (f) and radius of curvature denoted by R are defined in the diagram at the right.

2. Explain what is magnification of a spherical mirror?

The magnification is said to be an increase in the image size which is produced by spherical mirrors with respect to the object size. It is said to be the ratio of the height of the image to the height of the object and is denoted as m.

3. Explain what the formula of a spherical mirror is?

However, we can say that as discussed above in the article that in the small-angle approximation the focal length of a spherical mirror is one-half the radius of curvature of the mirror. or we can say that f=R/2. The mirror equation: 1do+1di=1f mirror equation.

4. Explain is a mirror a convex?

Both the center of focal point and the curvature are located on the side of the mirror opposite the object. As the focal point is generally located behind the convex mirror we can say that a mirror is said to have a negative focal length value.