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Spherical Mirror Formula
Spherical mirrors are those which contain a curved surface. These mirrors contain a layer of paint from one side to the remaining plane. Due to this paint, the light does not pass from this mirror and is reflected.
About the Topic
The spherical mirrors are of two types. These are convex mirrors and concave mirrors. Convex mirrors are those spherical mirrors whose inward surface or convergence was painted.
On the other hand, the concave mirror is a spherical mirror whose outer surface or bulging surface is painted.
Convex mirrors are called converging mirrors, while concave mirrors are called with the name of diverging mirrors.
It’s all about the spherical mirror. Let’s come to the spherical mirror formula. The spherical mirror is used to demonstrate the relation between object and image with the mirror’s focal length. The object distance in the formula of a spherical mirror defines the numerical value of the distance between the object and the mirror’s centre. At the same time, the image distance in the formula of a spherical mirror defines the numerical value of the distance between the image and the centre of the mirror. The focal length is the distance between the principal focus and the centre of the spherical mirror. So, these three quantities are used for demonstrating the spherical mirror formula.
Formula
1/v + 1/u = 1/f
v = Distance between the image and centre of the spherical mirror
u = Distance between the object and centre of the spherical mirror
f = Distance between the principal focus and the center of the spherical mirror
Solved Examples
1. Find the focal length of the spherical mirror, if the image distance is 4 cm and the object distance is 3 cm.
Image distance, v = 4cm
Object distance, u = 3cm
Using the mirror formula,
1/v + 1/u = 1/f
1/4 + 1/3 = 1/f
(3 + 4)/12 = 1/f
7/12 = 1/f
On Reciprocal,
f = 12/7
f = 1.71 cm
2. Find the object distance of the spherical mirror, if the image distance is 3 cm and the focal length is 5 cm.
Image distance, v = 3cm
Focal length, f = 5cm
Using the mirror formula,
1/v + 1/u = 1/f
1/3 + 1/u = 1/5
1/u = 1/5 – 1/3
1/u = (3+5)/15
1/u = 8/15
On Reciprocal,
u = 15/8
u = 1.87 cm
