General terms related to spherical mirrors: A mirror with the shape of a portion cut out of a spherical surface or substance is known as a...

General Terms Related to Spherical Mirrors

April 11, 2024**Light**: We can see the world around us during the daytime, but it is very difficult to see the things around us on a moonless night when it is dark outside. It is because during the daytime there is sunlight and on most nights we have a moon in the sky. Sun is the major source of light. We see an object when light enters our eyes after reflection from that object. This is why we can see the moon too! Light from the sun is reflected by the moon, which lights up the night sky. The twinkling of stars is a magic trick that light plays with our eyes as it travels through different layers of the earth’s atmosphere.

Light generally travels in a straight line path to form sharp shadows of various objects; although its path may bend around certain very small objects kept in its path, such a bending of its path is called diffraction. Most of the phenomena that we observe in our daily lives can be explained by the straight-line motion of light. To help us understand these phenomena, let’s look at reflection, refraction, and image formation by mirrors and lenses.

The change in the direction of light as it strikes a highly polished surface like a mirror is known as the reflection of light.

**The two laws of reflection are**:

- The angle of incidence is equal to the angle of reflection.
- The incident ray, the reflected ray, and the normal to the mirror at the point of incidence lie in the same plane.

The mirrors which have their reflecting surfaces curved are called spherical mirrors. Such mirrors can be considered to form a part of the surface of a sphere.

**Concave mirror**: A spherical mirror whose reflecting surface is curved inwards.

**Convex mirror**: A spherical mirror whose reflecting surface is curved outwards.

Refer to the diagram; the blue shaded curve is the reflecting surface for each mirror. The incident rays strike from the left for both mirrors. Terms related to spherical mirrors:

**Pole**: It is a point that lies at the centre of the reflecting surface of a spherical mirror. The letter \(P\) represents it.

**Centre of curvature**: It is the center of the sphere of which the spherical mirror forms a part. It is represented by the letter \(C\). It lies outside its reflecting surface. For a concave mirror, \(C\) lies in front of the mirror. For a convex mirror, \(C\) lies behind the mirror.

**The radius of curvature**: The radius of the sphere of which the reflecting surface forms a part. The letter \(R\) represents it.

**Principal Axis**: A straight line that passes through the pole and centre of curvature of the reflecting spherical surface.

**Principal focus**: Rays parallel to the principal axis incident on a concave/convex mirror converge-to/diverge-from a point on the principal axis. This point is called the principal focus. It is represented by the letter \(F\).

**Focal length**: It is the distance between the pole and the principal focus of a spherical mirror. It is represented by the letter \(f\).

**Aperture**: The diameter of the reflecting surface of a spherical mirror is called the aperture. It is basically the size of the mirror.

For spherical mirrors with small apertures, \(R=2f\), i.e. the principal focus lies midway between the pole and centre of curvature.

Each extended object kept in front of a spherical mirror can be considered to be composed of finite point–sized objects. To obtain an image formed by a spherical mirror, we need at least two reflected rays from the point object, and at the intersection of the two rays, an image will be formed. Follow these rules of reflection to obtain the image:

1. After reflection, a ray of light moving parallel to the principal axis will converge to or appear to diverge from the principal focus.

2. A ray of light passing through the principal focus or moving towards the principal focus, after reflection, will move parallel to the principal axis.

3. A ray of light passing through or moving towards the centre of curvature or appears to be coming from the centre of curvature, after reflection, retraces its path.

4. A ray of light incident obliquely at the pole of a spherical mirror is reflected obliquely.

The following table tells us the size and location of the image formed for the object kept at various locations in front of a concave mirror.

Position of object | Position of Image | Nature of image |

At infinity | At focus | Real, inverted and point-sized |

Between infinity and centre of curvature | Between \(C\) and \(F\) | Real, inverted and smaller in size compared to object |

At centre of curvature | At centre of curvature | Real, inverted and same-sized |

Between centre of curvature and focus | Between infinity and centre of curvature | Real, inverted and enlarged |

At focus | At infinity | Real, inverted and infinitely large |

Between focus and pole | Behind the mirror | Virtual, erect and enlarged |

These are used to get powerful parallel beams of light in torches, searchlights and vehicles headlights, and they are often used as shaving mirrors to obtain a larger image of the face. In solar furnaces, large concave mirrors are used to concentrate sunlight to produce a large amount of heat.

The following table tells us the size and location of the image formed for the object kept at various locations in front of a convex mirror.

Position of object | Position of image | Nature of image |

Between infinity and pole | Behind the mirror between pole and focus | Virtual, erect smaller than the object |

At infinity | At focus | Virtual, erect and point-sized |

Convex mirrors are used as rearview mirrors in vehicles. As these mirrors form images smaller than the objects(they shrink the objects), they provide a wider field of view. In other words, you can see more(like zooming out on your phone camera)! You can see nearly all of what’s behind the car using a rearview mirror.

\(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\)

Here,

\(v:\) Image distance

\(u:\) Object distance

\(f:\) Focal length

**Magnification of mirror**: It gives the extent to which the image of an object is magnified with respect to an object.

\(m=\frac{\text { height of } image}{\text { height of object }}=\frac{\hbar^{\prime}}{h}=-\frac{y}{u}\)

Magnification is negative in the case of a real image and positive for a virtual image.

The change in the direction of propagation of light as it travels obliquely from one medium into another is known as the refraction of light. This bending of light from one medium to another takes place due to the different speeds of light in different media.

- The incident ray, the refracted ray and the normal to the interface of the two transparent media at the point of incidence all lie in the same plane.
- For the light of given colour, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant in the given pair of media. This is known as Snell’s law of Refraction. It is true for the angle of incidence \((i), 0^{\circ}<i<90^{\circ}\)

According to this law,

\(\frac{{\sin i}}{{\sin r}} = \) constant —(1)

Where \(r\) is the angle of refraction.

The constant in equation \((1)\) is the refractive index of medium \(2\) w.r.t medium \(1\) denoted by \(n_{21}\)

The refractive index of medium \(2\) with respect to medium \(1\) is equal to the ratio of the speed of light in medium \(1\) to the speed of light in medium \(2\). If \(v_{1}\) and \(v_{2}\) be the speed of light in medium \(1\) and \(2\), respectively.

\(n_{21}=\frac{\text { speed of light in mediun } 1}{\text { speed of light in medium } 2}=\frac{v_{1}}{v_{2}}\)

If medium \(1\) is vacuum or air, the refractive index of medium \(2\) with respect to vacuum is called the absolute refractive index of medium \(2\). It can be given as:

\(n_{2}=\frac{\text { speed of light in air }}{\text { speed of light in medium } 2}=\frac{c}{v_{2}}\)

This is the formula for the refractive index of the medium \(2\).

A lens is a transparent material bound by two surfaces in which either surface or both are spherical.

**Convex lens**: A lens bound by two spherical surfaces, both of them bulging outwards, is known as a double convex or simply convex lens. This lens is thicker in the middle than at the edges. This lens converges light rays falling on it, and hence it is called a converging lens.

**Concave lens**: A lens bound by two spherical surfaces, both of them curved inwards, is known as a double concave or simply concave lens. It is thicker at the edges than at the middle. This lens diverges light rays falling on it, and hence it is called a diverging lens.

Each convex and concave lens consists of two spherical surfaces, and each of these surfaces is a part of a sphere. Centres of these spheres are called centres of curvature of the lens and can be represented by \(C_{1}\) and \(C_{2}\)

**Principal axis**: An imaginary axis passing through the two centres of curvature of a lens is known as the principal axis.

**Optical centre**: The central point of a spherical lens is called its optical centre, and a ray passing through the optical centre is undeviated; its trajectory remains the same.

**Aperture**: It is the effective diameter of the circular outline of a spherical lens. For thin lenses, the aperture is small.

**Principal focus**: The rays coming parallel to the principal axis of a convex lens/concave lens converges to or appears to diverge from a point on the principal axis; this point is called the principal focus. Each of these lenses has two foci \(F_{1}\) and \(F_{2}\)

**Focal length**: The distance between the optical centre and principal focus is called the focal length.

The image formation by lenses requires a minimum of two light rays, and for drawing the ray diagram, we can use the following rules:

1. A ray of light moving parallel to the principal axis, after refraction, converges to or appears to diverge from the principal focus.

2. A ray of light passing through or moving towards the principal focus, after refraction, moves parallel to the principal axis.

3. A ray of light passing through the optical center is undeviated.

The nature, size and position of the image formed by a convex lens for various positions of an object kept in front of it are given in the table below:

Position of object | Position of Image | Nature of image |

At infinity | At \(F\) | Real, inverted and highly diminished |

Between infinity and \(2F\) | Between \(F\) and \(2F\) | Real, inverted and diminished |

At \(2F\) | At \(2F\) | Real, inverted and same-sized |

Between \(2F\) and \(F\) | Between \(2F\) and infinity | Real, inverted and enlarged |

At \(F\) | At infinity | Real, inverted and infinitely large |

Between \(F\) and optical centre | Same side as that of the object | Virtual, erect and enlarged |

The nature, size and position of the image formed by a concave lens for various positions of an object kept in front of it are given in the table below:

Position of object | Position of image | Nature of image |

Between infinity and optical centre | Between F and optical centre | Virtual, erect and diminished |

At infinity | At \(F\) | Virtual, erect and highly diminished |

We can conclude that concave lens forms a virtual, erect and diminished image of the object for all object positions.

\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)

Here,

\(v:\) Image distance

\(u:\) Object distance

\(f:\) Focal length

**Magnification of lens**: It gives the extent to which the image of an object is magnified with respect to an object.

\(m=\frac{\text { height of image }}{\text { height of object }}=\frac{h^{\prime}}{h}=\frac{y}{u}\)

The power of a lens is defined as the degree of the convergence or divergence of light rays achieved by the given lens. It is represented by \(P\) and is equal to the reciprocal of the focal length \((f)\). Mathematically,

\(P=\frac{1}{f}\)

The SI unit of power is a diopter. One diopter is the power of a lens with a focal length of one meter. The power of the convex lens is positive, and that of the concave lens is negative.

Here are some frequently asked questions about the CBSE Class 10 Chapter Light- Reflection and Refraction:

**Ans:** A spherical mirror is a part of a sphere. The radius of the sphere of which the mirror is a part is called the radius of curvature of that mirror.

**Ans: **A pencil dipped in a glass of water appears broken at the water-air interface due to the refraction of light.

**Ans:** The SI unit of power is diopter.

**Ans:** Embibe provides 3D videos with real-life examples to help students learn the CBSE Class 10 Chapter Light.

**Ans:** Students can practice numerous questions on Embibe for CBSE Class 10 Chapter Light.

*We hope this detailed article on the concept of Light helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!*