Lenses are part of a transparent spherical mirror. They disperse light by the phenomenon of refraction — the process by which light rays deflect while passing from one medium to another medium). Lenses can be primarily of two types: Convex (converging) lens and Concave (diverging) lens. Silvering the surface of such lenses causes the formation of the mirror. The light rays fall on the mirror and reflect, forming the image in the viewer’s eye. In back-silvered mirrors (the most common), the light reaches the reflecting surface after going through the glass.

Moreover, one can also observe a protective layer at the back of this reflecting surface. This protective layer prevents scratches and corrosion on the fragile reflecting surface of the mirror. The glass layer absorbs some light in such mirrors, causing blurred images. Therefore, the reflecting surface is on the surface, i.e., towards the light source, to obtain better clarity. Such mirrors are ‘front-silvered’.

Types of Lens

The lens is a transparent material with either one or both surfaces spherical and at least one or both sides curved. As already stated above, a lens is part of a spherical mirror with two primary lens categories.

1. Convex Lens: The convex lens is converging, thick at the centre but thin at the edges. They are called converging lenses because they cause the incident parallel light rays to converge at a point. The convex lens is further categorised into three sub-categories. These categories are:

• Double-Convex Lens: These are the lens types that possess convex surfaces. 
• Plano-Convex Lens: As the name suggests, this lens has one planar side accompanied by a convex side.
• Concavo-Convex Lens: This type of lens possesses one concave and the other convex side.

1. Concave Lens: The concave lens is the diverging lens, thin at the centre but thick at the edges. They are called diverging lenses because they cause the incident parallel light rays to diverge from a point. The concave lens is further categorised into three sub-categories. These categories are:

• Double-Concave Lens: These types of lenses possess both concave surfaces.
• Plano-Concave Lens: As the name suggests, this lens has one planar side accompanied by a concave side.
• Convexo-Concave Lens: Similarly, this type of lens possesses one concave and the other convex side.

Silvering to Manufacture Mirrors

Electroplating is one of the most common methods for silvering lenses for making mirrors in modern times. Other methods are vacuum deposition and wet processes. For electroplating the given glass, a thin layer of conductive and transparent medium is deposited over the surface, reducing the adhesion between the material and the metal. The vacuum deposition method creates a very thin and uniform coating over the surface.

Examples of Silvering 

The types of metals used in silvering are:

Aluminium: In optical instruments such as telescopes.

Gold: Usually in infrared instruments.

Tin: Tin-coated glass mirrors by applying tin-mercury amalgam on the surface and evaporating the mercury.

Focal Length of the Silvered Lens

The focal length (distance between the focus and the centre of the lens) of the silvered lens is as follows:

1F= 2fl+1fm

fl= Focal length of the lens (from where refraction takes place).

fm= Focal length of the lens (from where reflection takes place).

Solved Questions on Lens and Mirrors

Q 1- Determine the two possible distances of an object from a concave mirror with a focal length of 20 cm. An object placed in front forms a three times larger image than the object. 

Solution: 

Suppose m as +3.

According to the data given in question:

m = f / f−u

3= -20 / -20-u 

20+u = 20/3

u =20/3 − 20 

u= 20−60 / 3

u = − 40/3 cm.

Suppose m as -3.

Then, m= f / f−u

−3= −20 / -20-u 

-3= 20 / 20+u

20 + u = 20 / −3

20+u = 20/-3

u = (20/-3) − 20

u = − 80/3 cm.

Answer: The two possible distances of an object from a concave mirror with a focal length of 20 cm will be 40/3 cm and − 80/3 cm.

Q 2- A convex lens forms a 4 times magnified image with a focal length of 20 cm, placed at a particular distance from the object. Determine this distance.

Solution:

According to the data given in question:

f=20 cm.

m=4.

Using the formula,

m = v/u 

4= v/u 

Or, v = 4u.

Using the lens equation, 

1/f =  1/v − 1/u or 1/f = 1/4u − 1/u

1/f = -3/4u

u = -3f 4 

u= − 3×20/4

u = − 15 cm.

Answer: The four times magnified image formed by a convex lens with a focal length of 20 cm is placed 15 cm from the object. 

Conclusion

A lens (part of spherical mirrors) disperses light rays falling on it by the phenomenon of refraction. There are two primary categories of lenses: convex and concave lenses. These lenses are sub-categorised into Double-convex, Plano-convex and Concave-convex. Similarly, the concave lens has three sub-divisions: Double-concave, Convexo-concave and Plano-concave lenses. The silvering of any surface of the lens creates a mirror. Mirrors can either be ‘back-silvered’ or ‘front-silvered’. Back silvered mirrors may create slightly blurry images. Electroplating is one of the most common methods for silvering lenses when producing mirrors. Other methods are vacuum deposition and wet processes.