# Optics: Overview, Questions, Preparation

Optics 2021 ( Optics )

1.2K Views
Updated on Jun 24, 2021 11:30 IST

## What is the Lens formula?

The lens formula can be described as the relationship between the focal length, the distance of an object, and the lens’ image. The lens formula is appropriate for both convex and concave lenses. The thickness of the lenses is negligible. The lens formula is as follows:

1/v – 1/v = 1/f

Here, v is the distance of an image

f is the focal length

u is the distance of an object.

## Derivation of lens formula

There are two types of lens, concave and convex lens.

Derivation on the convex lens:

Let us consider a convex lens having an optical center as O, F being the principal focus.

So, A’B’/AB = OB’/OB

The triangles ΔABO and ΔA’B’O are similar to each other

In the same way, ΔA’B’F and ΔOCF are similar to each other

So, A’B’/OC = FB’/OF

Now, OC = AB

So, A’B’/AB = FB’/OF

From the above equations, we can get,

OB’/OB = FB’/OF = (OB’ – OF) / OF

Using sign convention,

OB = -u, OB’ = v and OF = f

We get, v/-u = (v-f) / f

Which means vf = -uv + uf

Or, uv = uf – vf

Hence, 1/f = 1/v + 1/u

Derivation on the concave lens:

Let us assume that the AB is perpendicular to the principal axis and the distance is f of the convex lens. Here, we can assume,

OF1 as focal length

OA as the distance of the object

OA as image distance,

And ΔOAB and ΔOA’B’ are equal to each other

Angle BAO = angle B’A’O = 90°, and O is common in both the angles.

So, angle AOB = angle A’OB’

Now, angle. ABO and A’B’O are equal

And, A’B’/AB = OA’/OA

So, A’B’/OC = A’F1/ OF1

Now from the above equations, we get,

OA’ / OA = (OF1 – OA’) OF1

-v / -u = (-f - - v) / -f

V / u = (-f + v) / -f

-vf = -uf +uv

Let us now divide the above equation by uvf

-1/ u = -1/v + 1/f

Hence, 1/f = 1/v – 1/u

And this is the formula of the concave lens.

## Derivation of lens formula for class 12

As per the new pattern 2021, the chapter ' Optics' holds a significant weightage of 7 marks. These 7 marks include 2 questions in total, one short question of 2 marks, and one long question of 5 marks.

## Illustrated examples

Example 1) Illustrate the lens formula for the convex lens.

Answer – The lens formula for convex lens is 1/f = 1/v + 1/u

Example 2) Write the sign of v in a concave lens.

Answer – The sign of v in the concave lens is positive due to the incident rays.

Example 3) Write the name of the lens used in the torchlight.

Answer – Torch lights use a diverging lens, also known as a concave lens to make the parallel light spread out evenly.

## FAQs on Derivation of lens formula

1) What is the lens formula?

Answer - The lens formula can be described as the relationship between the focal length, a distance of an object, and the distance of an image of the lens.

2) What is the SI unit of the lens?

Answer – The SI unit of the lens is Dioptre or diopter. 1 dioptre is equal to 1 m -1 .

3) What is the difference between mirror and lens?

Answer – The mirror can be straight or round in shape and can be formed into different shapes whereas lenses are curved from the surfaces

4) What lens or mirrors are used by the dentists?

Answer – Dentists use the concave mirror to get magnified and clear reflection of the mouth. They refract the light to see the zoomed-in image.

5) What lenses are used in the street lights?

Answer – Street lights use convex mirrors because the convex mirror reflects the light, and it spreads it in the broader area.

Latest NewsPopular News

### JEE Main 2024 Application Form Available till November 30; Apply Now at jeemain.nta.ac.in

Mamona MajumderNov 28, 2023 15:27 IST

### How to Fill VIT Vellore Application Form 2024? Check Dates, Steps and More Details

Saakshi Varsha LamaNov 28, 2023 15:19 IST

### CTET 2024 Application Concluded @ctet.nic.in Live: Form correction window opens soon; check dates here

Rupali PruthiNov 28, 2023 15:19 IST

### CAT 2023 Live Updates (Slot 1, 2 & 3); Question Paper Analysis (Available), Answer Key, Expected Cutoffs

Vipra ShrivastavaNov 28, 2023 15:06 IST

### UGC NET Admit Card 2023: NTA NET JRF Hall Ticket, Expected Date, Exam Schedule, Direct Link @ugcnet.nta.nic.in

Dewesh Nandan PrasadNov 28, 2023 15:02 IST

Satyendra SinghNov 28, 2023 14:42 IST

### List of NIT Colleges in India 2024 - NIRF Ranking, Courses, Seats, Cutoff, Fees and Placement

Satyendra SinghNov 1, 2023 16:34 IST

### JEE Main 2024 Marks vs Percentile vs Rank

Satyendra SinghNov 28, 2023 14:38 IST

### NEET Chapter Wise Weightage 2024 PDF by NTA: Physics, Chemistry & Biology

Sreetama Datta RoySep 21, 2023 16:41 IST

### List of Top IITs in India 2024: NIRF Ranking, Courses, Seats, Fees & Placement

Satyendra SinghNov 1, 2023 16:33 IST

### Top 80 Group Discussion (GD) Topics 2023: Check Current & Latest GD Topics for MBA

Vipra ShrivastavaOct 3, 2023 12:10 IST

Optics Exam

### Student Forum

Anything you would want to ask experts?
Write here...