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Mirror Formula for Spherical Mirrors - Detailed Guide

Mirror Formula for Spherical Mirrors - Detailed Guide

Team Careers360Updated on 02 Jul 2025, 05:04 PM IST

In this article we are going to learn about the formula for spherical mirror ,sign convention for concave mirror, sign convention for convex mirror and also the sign convention for spherical lenses.
A spherical refracting surface is the part of a sphere separating two transparent media .There are two types of spherical refracting surfaces.

  • Concave spherical refracting surface
Mirror Formula for Spherical Mirrors - Detailed Guide
Mirror Formula for Spherical Mirrors

Concave spherical refracting surface

  • Convex spherical refracting surface

Convex spherical refracting surface

The spherical refracting surfaces have such components:

spherical refracting surfaces

  • Pole : The midpoint of a spherical refracting surface is called pole of the spherical surface.
  • Centre of curvature : The centre of the sphere which forms a curved refracting surface , is known as centre of curvature.
  • Radius of curvature : The radius of the sphere of which the refracting surface is a part is called the radius of curvature.
  • Principal axis : The straight line joining the pole and the centre of curvature of the spherical refracting surface and the extended on both sides is called the principal axis of the surface.
  • Aperture: The effective diameter of the refracting spherical surface exposed to the incident light is called the aperture.

Also read -

What is sign convention?

It is a selection of physical significance of signs for a particular quantity.

For sign convention we need to follow some assumptions/write the rules for sign convention:

The refraction through the spherical surface follows the following assumptions

  • The object has to be a point object and it will lie on the principal axis.
  • The aperture has to be small on the spherical refracting surface.
  • Refraction of paraxial rays will be considered only.

Related Topics Link,

Sign convention for mirror/sign convention for spherical mirror/ sign convention for reflection by spherical mirror:

  1. If the principal axis of the spherical reflecting surface is x-axis and distances along the y-axis above the principal axis, then the principal axis is taken as a positive sign and the y axis below the x-axis is taken as a negative sign.
  2. All distances are measured from the pole of the spherical surface.
  3. The distance measured from the pole in the direction opposite to the direction of the incident ray is taken as a negative sign and the measured direction of the incident ray is taken as a positive sign.
  4. The sign convention for a convex lens and concave mirror is the same.
  5. The sign convention for a concave lens and a convex mirror is the same.
  • Relation between focal length (f) and radius of curvature (r) :
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r=2f

  • The general equation for lens / spherical mirror formula:

1/v+1/u=1/f

Where v is the image distance, u is the object distance f is the focal length of the lens.

This is also the formula for conjugate foci.

  • Linear magnification formula :

m=-v/u

m is the linear magnification of the lens.

Linear magnification can also be the ratio of the height of the image to the height of the object.

m=I/O

=length or height of the image / length or height of the object

  • Longitudinal or axial magnification:

mA=length of the image along the principal axis / length of the object along the principal axis

The spherical mirror longitudinal magnification is equal to the square of the linear magnification.

mA=m2

  • The general form of refraction of light at the common spherical surface is when the light rays move from medium 1 to medium 2.

\frac{\mu_2}{v}-\frac{\mu_1}{u}=\frac{\mu_2-\mu_1}{R}

µ1 = refractive index of medium 1

µ2 = refractive index of medium 2

R = radius of curvature of a spherical surface.

Also Read:

xy=f2

Where, x = u – f ; y = v – f

  • Lens maker’s formula :

\frac{1}{f}=(\mu-1)(\frac{1}{r_1}-\frac{1}{r_2})

Where = refractive index of the material of the lens with respect to the surrounding medium.

r1= radius of curvature of the medium 1 ;

r2 = radius of curvature of the medium 2.

  • Power of a lens:

Power can be expressed as:

P=1/f

Here, f is focal length (meters) and D is the unit of power which is measured in dioptre.

Also check-

NCERT Physics Notes:

Commonly Asked Questions

Q: How does the mirror formula differ for concave and convex mirrors?
A:
The mirror formula (1/f = 1/v + 1/u) remains the same for both concave and convex mirrors. However, the sign conventions for u, v, and f differ. For concave mirrors, f is positive, while for convex mirrors, f is negative.
Q: What are the sign conventions used in the mirror formula?
A:
The sign conventions are: (1) All distances are measured from the pole of the mirror. (2) Distances measured in the direction of incident light are positive. (3) Distances measured against the direction of incident light are negative. (4) Heights above the principal axis are positive, and below are negative.
Q: Why is the focal length of a convex mirror always negative?
A:
The focal length of a convex mirror is always negative because its focus is located behind the mirror surface, in the virtual space. This is consistent with the sign convention where distances measured opposite to the direction of incident light are considered negative.
Q: Can the mirror formula be used to predict whether an image will be real or virtual?
A:
Yes, the mirror formula can help predict if an image is real or virtual. If the calculated value of v is positive, the image is real and on the same side as the reflected rays. If v is negative, the image is virtual and behind the mirror.
Q: How does the mirror formula apply to plane mirrors?
A:
For plane mirrors, the focal length (f) is infinite. Applying this to the mirror formula (1/f = 1/v + 1/u) gives 1/∞ = 1/v + 1/u, which simplifies to v = -u. This means the image distance is equal to the object distance but on the opposite side of the mirror.

Frequently Asked Questions (FAQs)

Q: How can the mirror formula be used to understand the concept of virtual focus in convex mirrors?
A:
For convex mirrors, the mirror formula uses a negative focal length, representing the virtual focus behind the mirror. This explains why convex mirrors always form virtual images and helps in calculating the position of these virtual images.
Q: How does the mirror formula relate to the concept of optical axis in spherical mirrors?
A:
The mirror formula assumes measurements along the optical (principal) axis. It helps in understanding how object and image positions relate to this axis, which is crucial for predicting image characteristics and understanding the symmetry of the optical system.
Q: Can the mirror formula predict when no image will be formed?
A:
Yes, the mirror formula can predict when no real image is formed. For instance, if the calculated value of v is negative for a concave mirror, it indicates that no real image is formed; instead, a virtual image is created behind the mirror.
Q: How does the mirror formula help in determining the nature of the image?
A:
The mirror formula helps determine the nature of the image by giving the image distance (v). If v is positive, the image is real; if negative, it's virtual. Combined with the magnification formula, it also indicates whether the image is upright or inverted.
Q: What is the significance of the 'New Cartesian Sign Convention' in the mirror formula?
A:
The New Cartesian Sign Convention provides a consistent system for assigning signs to distances in the mirror formula. It helps in correctly applying the formula and interpreting its results, ensuring that the calculations accurately represent the physical reality of image formation.
Q: How does the mirror formula help in understanding the concept of virtual focus in convex mirrors?
A:
For convex mirrors, the mirror formula uses a negative focal length, representing the virtual focus behind the mirror. This negative f in the equation (1/f = 1/v + 1/u) helps explain why convex mirrors always form virtual, upright images regardless of object position.
Q: What is the relationship between the mirror formula and the thin lens formula?
A:
The mirror formula (1/f = 1/v + 1/u) is mathematically identical to the thin lens formula. The main difference is in the sign conventions used and the physical interpretation of the terms, as mirrors reflect light while lenses refract it.
Q: Can the mirror formula be used to explain why convex mirrors always produce virtual images?
A:
Yes, the mirror formula explains this. For convex mirrors, f is negative. No matter what positive value of u is used, v will always be negative (indicating a virtual image) when solved in the equation 1/f = 1/v + 1/u, where f is negative.
Q: How does the mirror formula relate to the concept of real and virtual images?
A:
The mirror formula helps distinguish between real and virtual images through the sign of v (image distance). A positive v indicates a real image formed in front of the mirror, while a negative v represents a virtual image behind the mirror.
Q: How does the mirror formula help in understanding the concept of virtual objects?
A:
While less common, virtual objects can be considered in the mirror formula by using a negative value for u. This situation might arise when dealing with multiple mirror systems or when analyzing the image from one mirror as the object for another.
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