## Power of lens

Category : 8th Class

### Power of a Lens

A lens either converges or diverges the ray of light. The ability of lens to convergeor diverge the ray of light is called the power of lens. The convex lens convergesthe ray of light and the concave lens diverges the ray of light. The power of thelens depends on the focal length of the lens. It is also defined as the reciprocalof the focal length. It is given by,

$Power=\frac{1}{Focal\,length},or\,\,\,P=\frac{1}{F}$

Here, P is the power of the lens and F is the focal length of the lens.

The unit of the power of the lens is Diopter. It denoted by D. One diopter is thepower of the lens whose focal length is one meter. If the focal length of thelens is positive, it is a convex lens, its power is positive. On the other hand, ifthe focal length of the lens is negative, it is a concave lens, the power isnegative.

If the number of lens is placed in close contact with each other, the power ofthe combination of the lenses is equal to the algebraic sum of the power of theindividual lens. Thus, if P1, P2, P3…….. , Pn are the powers of n-lens, the resultantpower is given by:

$P={{P}_{1}}+{{P}_{2}}+{{P}_{3}}+---{{P}_{n}}$

Two lens of power 4.5 D and - 3.5 D are combined together. Find thepower and the focal length of the combined lens.

(a) 2 D and 1m

(b) 3D and 2m

(c) ID and 1m

(d) 2 D and 2 m

(e) None of these

Explanation

The combined power of the number of lens is equal to the sum of theindividual powers of the lens.

A convex lens of focal length 40 cm and a concave lens of focal length200 cm are placed in contact with each other. Find the power of thecombined lens.

(a) 2 D

(b) 3 D

(c) 1.5 D

(d) 2.5 D

(e) None of these

Explanation

On calculation we find that the combined power of the lens is 2 D.

Dispersion of Light

We know that the white light consists of seven colours. When it is passedthrough a prism, it splits into its constituent colours known as VIBGYOR. Thisband of seven colours is called spectrum. The seven colours of the spectrumare violet, indigo, blue, green, yellow, orange, and red. The red colour is at thetop of the spectrum, while the violet colour is at the bottom of the spectrum.The dispersion of white light as it passes through the prism is due to thedifference in the angle of refraction of light, of different colour. The sequenceof the colours in the spectrum are in the decreasing order of their wavelengthfrom top to bottom. One of the various effects of the dispersion is the formationof rainbow in the sky, after rain.

Dispersion of Light

Atmospheric Refraction

The refraction of light, caused by the atmosphere due to difference in the densityof different layers of the atmosphere, is called the atmospheric refraction. Thevarious phenomena of the atmospheric refractions are twinkling of stars,advanced sunrise and sunset, appearance of the Sun red at the time of sunrise and sun set etc.

Another important characteristic of light is the scattering of light. When thelight strikes any particle object in its path, it gets scattered into differentdirections. This is known as the scattering of light. The sky appears blue; thisis one of the effect of the scattering of light. When the sunlight enters in ouratmosphere, lights of the longer wavelength do not get scattered by the airmolecule in the atmosphere and passes straight through it. On the other hand,lights of shorter wavelength, i.e. blue colour get scattered all around in thesky by the air molecules present in the atmosphere. Hence, the sky appearsblue to our eyes.

When the light strikes the particles in its way, it undergoes scattering.There are many such events in which the scattering of light takesplace. What is the colour of the sunlight, scattered by the dust particlein the atmosphere?

(a) Red

(b) Blue

(c) Yellow

(d) Green

(e) None of these

Explanation

The blue colour has shorter wavelength and is scattered most by theparticles in the atmosphere.

We see the Sun before and after its scheduled time of sunrise andsunset respectively. It is because of the atmospheric refraction. Whatis the duration of advanced sunrise or delayed sunset?

(a) 1 minutes

(b) 2 minutes

(c) 3 minutes

(d) 4 minutes

(e) None of these

Explanation

The duration of advanced sunrise and delayed sunset is 2 minutes.

• The speed of sound is generally about 186,000 miles per second.
• The light takes about 8 minutes and 17 second to reach earth form the Sun.
• In one second nearly 100 lightning bolts strike the Earth.
• Nearly 1000 people are killed around the world due to lightning.
• Light is made up of electromagnetic radiations and always travels in straightlines.

• Light always travels in a straight line due to its transverse nature.
• The image formed in case of mirror and lens is either real or virtual,depending on the position of the object.
• There are two laws of light, i.e. reflection and refraction.
• While doing calculation on numerical problems on mirrorformula and lensformula, we must take care of sign convention.
• The magnification is equal to the ratio of height of image to the height ofobject.
• If the ray of light travels from rarer medium to denser medium, it bendstowards the normal and vice-versa.
• The speed of light in vacuum is 3 x 108 m/sec.
• The refractive index is the ratio of speed of light in one medium to thespeed of light in another medium.
• Power of lens is the reciprocal of its focal length.

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