Power of a mirror and lens, physical interpretation, Practice problems, FAQs

In physics, power is the capacity of doing some work with respect to time. As mirrors and lenses either converge or diverge the light ray, so the work for a mirror and lens is either to converge a ray or diverge a ray. Hence the power of a lens is the capacity of converging or diverging the rays. For example concave mirrors converge the light rays; if it converges more it will have more power than which converges less. Power depends upon the focal length of the optical device. Lets understand the relation with focal length.

Table of content

• Introduction
• Physical interpretation of the formula of optical power
• Power of Concave mirror
• Power of Convex mirror
• Power of Convex lens
• Power of Concave lens
• Relation between power and radius of curvature of lens
• Practice problems
• FAQs

Introduction

Power is the ability of mirrors and lenses to converge or diverge the path of rays of light.

The ability to converge or diverge (power) is inversely proportional to the focal length.

Ability to converge or diverge

• f should be in meters.
• The unit of power is dioptre (D).

Physical interpretation of the formula of optical power

Suppose a parallel beam of light is incident on two converging lenses. Let's say lens 1 has a focal length of 10 cm and lens 2 has a focal length of 20 cm as shown in the figure.

It can be seen from the figure that the light converges closer to lens 1 than lens 2. Therefore, it can be said that lens 1 has a higher power of convergence than lens 2. In conclusion, it can be said that the lower the focal length, the higher the optical power, or vice versa. Therefore, the focal length of an optical system must have the inverse proportionality with the optical power.

Power of Concave mirror

We know that a concave mirror converges the ray, the focal length is negative.

Optical Power of mirror is given by,

As focal length of concave mirror is negative, so power

Positive power means the mirror is of converging type.

Power of Convex mirror

A convex mirror diverges the rays that fall on it. Also, the focal length is positive.

Optical Power of mirror is given by,

As focal length of convex mirror is Positive, so Power

Negative power means the mirror is of Diverging type.

Power of Convex lens

A convex lens converges the rays that fall on it. And the focal length is positive.

Optical Power of lens is given by,

As focal length of convex lens is Positive, so Power

Positive power means the lens is of converging type.

Power of Concave lens

A concave lens diverges the ray, and the focal length is negative.

Optical Power of lens is given by,

As focal length of concave lens is negative, so Power

Negative power means the lens is of Diverging type.

Optical system	Formula of optical power	Types of optical systems	Corresponding focal length	Corresponding power
Mirror		Converging mirror (Concave mirror)	Negative	Positive
		Diverging mirror (Convex mirror)	Positive	Negative
Lens		Converging lens (Convex lens)	Positive	Positive
		Diverging lens (Concave lens)	Negative	Negative

Relation between power and radius of curvature of lens

The power of a lens is the reciprocal of the focal length of the lens.

According to the lens maker’s formula,

From eq and

This formula can be used to find power when radius of curvature and refractive index of material is given.

Practice problems

Q. A convex lens has a focal length of 20 cm. What is the power of lens in Dioptres?

A. Given focal length F = 20 cm = 0.2 m

Power of lens is given by,

Power of the convex lens is +ve. 

Q. A convex lens of power +4 D and a concave lens of power 3 D are placed in contact. Find the equivalent power of the combination ?

A. Given and

Equivalent power of the combination is 1 D.

Q. Find the power of a plano-convex lens, when the radius of a curved surface is 15 cm and refractive index of material is 1.5.

A. Given , cm and

Power of plano convex mirror can be calculated by 

Ans.

Here power is positive. So the lens will behave as a converging type.

Q. A 5 D lens forms a virtual image which is 4 times the object placed perpendicularly on the principal axis of the lens. Find the distance of the object from the lens.

A. Given power P = 5 D

Power of lens is given by,

Since the focal length is positive, the lens is a converging lens.

Now, we know that a virtual magnified image is formed by a converging lens if and only if the object is placed in between the focus and the optical center, i.e., the distance of the object from the optical center should be less than 20 cm.

It is also given that,

Let the distance of the object from the optical center be d so that u = -d

From the definition of the transverse magnification, we know the following:

Now, by applying the lens formula, we get,

Hence, u = -15 cm

Therefore, the object should be placed at 15 cm to the left of the convex lens.

FAQs

Q. What is the significance of the power of the lens?
A. Power is the ability to bend the ray of light. It can be used to correct defects in the eye by appropriately bending the light.

Q. Power of the lens greater in air or water?
A. In air the difference of refractive index between air and lens is greater and has the ability to bend the rays more, so have more power in air than water.

Q. What is the power of a plane slab of glass?
A. As the plane slab has both radius of curvature infinity, so power will be zero.

Q. Which convex lens,thick or thin, has more power?
A. A thick convex lens has less focal length, so will have more power than a thin lens.